id	sid	tid	token	lemma	pos
ejpam-3153	1	1	european	european	PROPN
ejpam-3153	1	2	journal	journal	PROPN
ejpam-3153	1	3	of	of	ADP
ejpam-3153	1	4	pure	pure	ADJ
ejpam-3153	1	5	and	and	CCONJ
ejpam-3153	1	6	applied	apply	VERB
ejpam-3153	1	7	mathematics	mathematic	NOUN
ejpam-3153	1	8	vol	vol	NOUN
ejpam-3153	1	9	.	.	PUNCT
ejpam-3153	2	1	11	11	NUM
ejpam-3153	2	2	,	,	PUNCT
ejpam-3153	2	3	no	no	INTJ
ejpam-3153	2	4	.	.	NOUN
ejpam-3153	2	5	1	1	NUM
ejpam-3153	2	6	,	,	PUNCT
ejpam-3153	2	7	2018	2018	NUM
ejpam-3153	2	8	,	,	PUNCT
ejpam-3153	2	9	69	69	NUM
ejpam-3153	2	10	-	-	SYM
ejpam-3153	2	11	78	78	NUM
ejpam-3153	2	12	issn	issn	PROPN
ejpam-3153	2	13	1307	1307	NUM
ejpam-3153	2	14	-	-	SYM
ejpam-3153	2	15	5543	5543	NUM
ejpam-3153	2	16	–	–	PUNCT
ejpam-3153	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3153	2	18	published	publish	VERB
ejpam-3153	2	19	by	by	ADP
ejpam-3153	2	20	new	new	PROPN
ejpam-3153	2	21	york	york	PROPN
ejpam-3153	2	22	business	business	PROPN
ejpam-3153	2	23	global	global	ADJ
ejpam-3153	2	24	application	application	NOUN
ejpam-3153	2	25	of	of	ADP
ejpam-3153	2	26	probabilistic	probabilistic	ADJ
ejpam-3153	2	27	method	method	NOUN
ejpam-3153	2	28	on	on	ADP
ejpam-3153	2	29	daehee	daehee	NOUN
ejpam-3153	2	30	sequences	sequence	NOUN
ejpam-3153	2	31	chang	chang	PROPN
ejpam-3153	2	32	liu1,∗	liu1,∗	PROPN
ejpam-3153	2	33	,	,	PUNCT
ejpam-3153	2	34	wuyungaowa1	wuyungaowa1	X
ejpam-3153	2	35	1	1	NUM
ejpam-3153	2	36	department	department	NOUN
ejpam-3153	2	37	of	of	ADP
ejpam-3153	2	38	mathematical	mathematical	ADJ
ejpam-3153	2	39	sciences	science	NOUN
ejpam-3153	2	40	,	,	PUNCT
ejpam-3153	2	41	inner	inner	PROPN
ejpam-3153	2	42	mongolia	mongolia	PROPN
ejpam-3153	2	43	university	university	PROPN
ejpam-3153	2	44	,	,	PUNCT
ejpam-3153	2	45	hohhot	hohhot	ADJ
ejpam-3153	2	46	,	,	PUNCT
ejpam-3153	2	47	inner	inner	ADJ
ejpam-3153	2	48	mongolia	mongolia	PROPN
ejpam-3153	2	49	,	,	PUNCT
ejpam-3153	2	50	p.r.china	p.r.china	ADJ
ejpam-3153	2	51	abstract	abstract	NOUN
ejpam-3153	2	52	.	.	PUNCT
ejpam-3153	3	1	in	in	ADP
ejpam-3153	3	2	this	this	DET
ejpam-3153	3	3	paper	paper	NOUN
ejpam-3153	3	4	,	,	PUNCT
ejpam-3153	3	5	we	we	PRON
ejpam-3153	3	6	investigate	investigate	VERB
ejpam-3153	3	7	some	some	DET
ejpam-3153	3	8	combinatorial	combinatorial	ADJ
ejpam-3153	3	9	sequences	sequence	NOUN
ejpam-3153	3	10	based	base	VERB
ejpam-3153	3	11	on	on	ADP
ejpam-3153	3	12	daehee	daehee	NOUN
ejpam-3153	3	13	and	and	CCONJ
ejpam-3153	3	14	changhee	changhee	VERB
ejpam-3153	3	15	numbers	number	NOUN
ejpam-3153	3	16	and	and	CCONJ
ejpam-3153	3	17	polynomials	polynomial	NOUN
ejpam-3153	3	18	,	,	PUNCT
ejpam-3153	3	19	then	then	ADV
ejpam-3153	3	20	derive	derive	VERB
ejpam-3153	3	21	their	their	PRON
ejpam-3153	3	22	moment	moment	NOUN
ejpam-3153	3	23	representations	representation	NOUN
ejpam-3153	3	24	in	in	ADP
ejpam-3153	3	25	use	use	NOUN
ejpam-3153	3	26	of	of	ADP
ejpam-3153	3	27	probabilistic	probabilistic	ADJ
ejpam-3153	3	28	method	method	NOUN
ejpam-3153	3	29	.	.	PUNCT
ejpam-3153	4	1	we	we	PRON
ejpam-3153	4	2	also	also	ADV
ejpam-3153	4	3	provide	provide	VERB
ejpam-3153	4	4	identities	identity	NOUN
ejpam-3153	4	5	related	relate	VERB
ejpam-3153	4	6	to	to	ADP
ejpam-3153	4	7	daehee	daehee	NOUN
ejpam-3153	4	8	numbers	number	NOUN
ejpam-3153	4	9	,	,	PUNCT
ejpam-3153	4	10	derangement	derangement	NOUN
ejpam-3153	4	11	numbers	number	NOUN
ejpam-3153	4	12	,	,	PUNCT
ejpam-3153	4	13	cauchy	cauchy	ADJ
ejpam-3153	4	14	numbers	number	NOUN
ejpam-3153	4	15	of	of	ADP
ejpam-3153	4	16	the	the	DET
ejpam-3153	4	17	second	second	ADJ
ejpam-3153	4	18	kind	kind	NOUN
ejpam-3153	4	19	,	,	PUNCT
ejpam-3153	4	20	and	and	CCONJ
ejpam-3153	4	21	stirling	stirling	NOUN
ejpam-3153	4	22	numbers	number	NOUN
ejpam-3153	4	23	of	of	ADP
ejpam-3153	4	24	the	the	DET
ejpam-3153	4	25	first	first	ADJ
ejpam-3153	4	26	kind	kind	NOUN
ejpam-3153	4	27	.	.	PUNCT
ejpam-3153	5	1	2010	2010	NUM
ejpam-3153	5	2	mathematics	mathematic	NOUN
ejpam-3153	5	3	subject	subject	NOUN
ejpam-3153	5	4	classifications	classification	NOUN
ejpam-3153	5	5	:	:	PUNCT
ejpam-3153	5	6	11b68	11b68	NUM
ejpam-3153	5	7	,	,	PUNCT
ejpam-3153	5	8	60e07	60e07	NUM
ejpam-3153	5	9	,	,	PUNCT
ejpam-3153	5	10	11b83	11b83	NUM
ejpam-3153	5	11	,	,	PUNCT
ejpam-3153	5	12	62e15	62e15	NUM
ejpam-3153	5	13	.	.	PUNCT
ejpam-3153	6	1	key	key	ADJ
ejpam-3153	6	2	words	word	NOUN
ejpam-3153	6	3	and	and	CCONJ
ejpam-3153	6	4	phrases	phrase	NOUN
ejpam-3153	6	5	:	:	PUNCT
ejpam-3153	6	6	moment	moment	NOUN
ejpam-3153	6	7	,	,	PUNCT
ejpam-3153	6	8	probabilistic	probabilistic	ADJ
ejpam-3153	6	9	method	method	NOUN
ejpam-3153	6	10	,	,	PUNCT
ejpam-3153	6	11	generating	generate	VERB
ejpam-3153	6	12	function	function	NOUN
ejpam-3153	6	13	,	,	PUNCT
ejpam-3153	6	14	daehee	daehee	NOUN
ejpam-3153	6	15	numbers	number	NOUN
ejpam-3153	6	16	,	,	PUNCT
ejpam-3153	6	17	changhee	changhee	NOUN
ejpam-3153	6	18	numbers	number	NOUN
ejpam-3153	6	19	.	.	PUNCT
ejpam-3153	7	1	1	1	X
ejpam-3153	7	2	.	.	X
ejpam-3153	7	3	introduction	introduction	NOUN
ejpam-3153	7	4	and	and	CCONJ
ejpam-3153	7	5	preliminaries	preliminary	NOUN
ejpam-3153	7	6	throughout	throughout	ADP
ejpam-3153	7	7	this	this	DET
ejpam-3153	7	8	paper	paper	NOUN
ejpam-3153	7	9	,	,	PUNCT
ejpam-3153	7	10	we	we	PRON
ejpam-3153	7	11	use	use	VERB
ejpam-3153	7	12	the	the	DET
ejpam-3153	7	13	following	following	ADJ
ejpam-3153	7	14	notations	notation	NOUN
ejpam-3153	7	15	:	:	PUNCT
ejpam-3153	7	16	n	n	X
ejpam-3153	7	17	=	=	SYM
ejpam-3153	7	18	{	{	PUNCT
ejpam-3153	7	19	1	1	NUM
ejpam-3153	7	20	,	,	PUNCT
ejpam-3153	7	21	2	2	NUM
ejpam-3153	7	22	,	,	PUNCT
ejpam-3153	7	23	3	3	NUM
ejpam-3153	7	24	,	,	PUNCT
ejpam-3153	7	25	·	·	PUNCT
ejpam-3153	7	26	·	·	PUNCT
ejpam-3153	7	27	·	·	PUNCT
ejpam-3153	7	28	}	}	PUNCT
ejpam-3153	7	29	,	,	PUNCT
ejpam-3153	7	30	z>0	z>0	NOUN
ejpam-3153	7	31	=	=	SYM
ejpam-3153	7	32	{	{	PUNCT
ejpam-3153	7	33	0	0	NUM
ejpam-3153	7	34	,	,	PUNCT
ejpam-3153	7	35	1	1	NUM
ejpam-3153	7	36	,	,	PUNCT
ejpam-3153	7	37	2	2	NUM
ejpam-3153	7	38	,	,	PUNCT
ejpam-3153	7	39	·	·	PUNCT
ejpam-3153	7	40	·	·	PUNCT
ejpam-3153	7	41	·	·	PUNCT
ejpam-3153	7	42	}	}	PUNCT
ejpam-3153	7	43	.	.	PUNCT
ejpam-3153	8	1	let	let	AUX
ejpam-3153	8	2	d	d	NOUN
ejpam-3153	8	3	(	(	PUNCT
ejpam-3153	8	4	k	k	NOUN
ejpam-3153	8	5	)	)	PUNCT
ejpam-3153	8	6	n	n	CCONJ
ejpam-3153	8	7	,	,	PUNCT
ejpam-3153	8	8	ξ(x	ξ(x	NOUN
ejpam-3153	8	9	)	)	PUNCT
ejpam-3153	8	10	denote	denote	VERB
ejpam-3153	8	11	the	the	DET
ejpam-3153	8	12	nth	nth	NOUN
ejpam-3153	8	13	twisted	twisted	ADJ
ejpam-3153	8	14	daehee	daehee	NOUN
ejpam-3153	8	15	polynomials	polynomial	NOUN
ejpam-3153	8	16	of	of	ADP
ejpam-3153	8	17	order	order	NOUN
ejpam-3153	8	18	k(∈	k(∈	VERB
ejpam-3153	8	19	n	n	CCONJ
ejpam-3153	8	20	)	)	PUNCT
ejpam-3153	8	21	,	,	PUNCT
ejpam-3153	8	22	which	which	PRON
ejpam-3153	8	23	are	be	AUX
ejpam-3153	8	24	defined	define	VERB
ejpam-3153	8	25	by	by	ADP
ejpam-3153	8	26	the	the	DET
ejpam-3153	8	27	generating	generating	NOUN
ejpam-3153	8	28	function[2	function[2	NOUN
ejpam-3153	8	29	]	]	PUNCT
ejpam-3153	8	30	to	to	PART
ejpam-3153	8	31	be	be	AUX
ejpam-3153	8	32	(	(	PUNCT
ejpam-3153	8	33	ln(1	ln(1	PROPN
ejpam-3153	8	34	+	+	NUM
ejpam-3153	8	35	ξt	ξt	X
ejpam-3153	8	36	)	)	PUNCT
ejpam-3153	8	37	ξt	ξt	NOUN
ejpam-3153	8	38	)	)	PUNCT
ejpam-3153	8	39	k(1	k(1	NOUN
ejpam-3153	8	40	+	+	CCONJ
ejpam-3153	9	1	ξt)x	ξt)x	PROPN
ejpam-3153	9	2	=	=	SYM
ejpam-3153	9	3	∞∑	∞∑	NUM
ejpam-3153	9	4	n=0	n=0	NUM
ejpam-3153	9	5	d	d	NOUN
ejpam-3153	9	6	(	(	PUNCT
ejpam-3153	9	7	k	k	NOUN
ejpam-3153	9	8	)	)	PUNCT
ejpam-3153	9	9	n	n	CCONJ
ejpam-3153	9	10	,	,	PUNCT
ejpam-3153	9	11	ξ(x	ξ(x	NOUN
ejpam-3153	9	12	)	)	PUNCT
ejpam-3153	9	13	tn	tn	PROPN
ejpam-3153	9	14	n	n	PROPN
ejpam-3153	9	15	!	!	PUNCT
ejpam-3153	9	16	.	.	PUNCT
ejpam-3153	10	1	(	(	PUNCT
ejpam-3153	10	2	1	1	X
ejpam-3153	10	3	)	)	PUNCT
ejpam-3153	10	4	in	in	ADP
ejpam-3153	10	5	special	special	ADJ
ejpam-3153	10	6	case	case	NOUN
ejpam-3153	10	7	,	,	PUNCT
ejpam-3153	10	8	when	when	SCONJ
ejpam-3153	10	9	x	x	X
ejpam-3153	10	10	=	=	SYM
ejpam-3153	10	11	0	0	NUM
ejpam-3153	10	12	,	,	PUNCT
ejpam-3153	10	13	d	d	X
ejpam-3153	10	14	(	(	PUNCT
ejpam-3153	10	15	k	k	NOUN
ejpam-3153	10	16	)	)	PUNCT
ejpam-3153	10	17	n	n	CCONJ
ejpam-3153	10	18	,	,	PUNCT
ejpam-3153	10	19	ξ	ξ	X
ejpam-3153	10	20	=	=	SYM
ejpam-3153	10	21	d	d	X
ejpam-3153	10	22	(	(	PUNCT
ejpam-3153	10	23	k	k	NOUN
ejpam-3153	10	24	)	)	PUNCT
ejpam-3153	10	25	n	n	CCONJ
ejpam-3153	10	26	,	,	PUNCT
ejpam-3153	10	27	ξ(0	ξ(0	NOUN
ejpam-3153	10	28	)	)	PUNCT
ejpam-3153	10	29	are	be	AUX
ejpam-3153	10	30	called	call	VERB
ejpam-3153	10	31	twisted	twisted	ADJ
ejpam-3153	10	32	daehee	daehee	NOUN
ejpam-3153	10	33	numbers	number	NOUN
ejpam-3153	10	34	of	of	ADP
ejpam-3153	10	35	order	order	NOUN
ejpam-3153	10	36	k.	k.	PROPN
ejpam-3153	10	37	similarly	similarly	ADV
ejpam-3153	10	38	,	,	PUNCT
ejpam-3153	10	39	d	d	PROPN
ejpam-3153	10	40	(	(	PUNCT
ejpam-3153	10	41	k	k	NOUN
ejpam-3153	10	42	)	)	PUNCT
ejpam-3153	10	43	n	n	NOUN
ejpam-3153	10	44	=	=	SYM
ejpam-3153	10	45	d	d	PROPN
ejpam-3153	10	46	(	(	PUNCT
ejpam-3153	10	47	k	k	NOUN
ejpam-3153	10	48	)	)	PUNCT
ejpam-3153	10	49	n,1	n,1	NOUN
ejpam-3153	10	50	are	be	AUX
ejpam-3153	10	51	higher	high	ADJ
ejpam-3153	10	52	-	-	PUNCT
ejpam-3153	10	53	order	order	NOUN
ejpam-3153	10	54	daehee	daehee	NOUN
ejpam-3153	10	55	numbers	number	NOUN
ejpam-3153	10	56	,	,	PUNCT
ejpam-3153	10	57	dn	dn	PROPN
ejpam-3153	10	58	,	,	PUNCT
ejpam-3153	10	59	ξ	ξ	PROPN
ejpam-3153	10	60	=	=	SYM
ejpam-3153	10	61	d	d	X
ejpam-3153	10	62	(	(	PUNCT
ejpam-3153	10	63	1	1	NUM
ejpam-3153	10	64	)	)	PUNCT
ejpam-3153	10	65	n	n	CCONJ
ejpam-3153	10	66	,	,	PUNCT
ejpam-3153	10	67	ξ	ξ	PROPN
ejpam-3153	10	68	are	be	AUX
ejpam-3153	10	69	twisted	twist	VERB
ejpam-3153	10	70	daehee	daehee	NOUN
ejpam-3153	10	71	numbers	number	NOUN
ejpam-3153	10	72	,	,	PUNCT
ejpam-3153	10	73	and	and	CCONJ
ejpam-3153	10	74	dn	dn	PROPN
ejpam-3153	10	75	=	=	SYM
ejpam-3153	10	76	d	d	PROPN
ejpam-3153	10	77	(	(	PUNCT
ejpam-3153	10	78	1	1	X
ejpam-3153	10	79	)	)	PUNCT
ejpam-3153	10	80	n,1	n,1	NOUN
ejpam-3153	10	81	are	be	AUX
ejpam-3153	10	82	daehee	daehee	NOUN
ejpam-3153	10	83	numbers	number	NOUN
ejpam-3153	10	84	.	.	PUNCT
ejpam-3153	11	1	let	let	VERB
ejpam-3153	11	2	d̂	d̂	PRON
ejpam-3153	11	3	(	(	PUNCT
ejpam-3153	11	4	k	k	NOUN
ejpam-3153	11	5	)	)	PUNCT
ejpam-3153	11	6	n	n	CCONJ
ejpam-3153	11	7	,	,	PUNCT
ejpam-3153	11	8	ξ(x	ξ(x	NOUN
ejpam-3153	11	9	)	)	PUNCT
ejpam-3153	11	10	denote	denote	VERB
ejpam-3153	11	11	the	the	DET
ejpam-3153	11	12	nth	nth	NOUN
ejpam-3153	11	13	twisted	twisted	ADJ
ejpam-3153	11	14	daehee	daehee	NOUN
ejpam-3153	11	15	polynomials	polynomial	NOUN
ejpam-3153	11	16	of	of	ADP
ejpam-3153	11	17	the	the	DET
ejpam-3153	11	18	second	second	ADJ
ejpam-3153	11	19	kind	kind	NOUN
ejpam-3153	11	20	of	of	ADP
ejpam-3153	11	21	order	order	NOUN
ejpam-3153	11	22	k(∈	k(∈	VERB
ejpam-3153	11	23	n	n	CCONJ
ejpam-3153	11	24	)	)	PUNCT
ejpam-3153	11	25	,	,	PUNCT
ejpam-3153	11	26	which	which	PRON
ejpam-3153	11	27	are	be	AUX
ejpam-3153	11	28	defined	define	VERB
ejpam-3153	11	29	by	by	ADP
ejpam-3153	11	30	the	the	DET
ejpam-3153	11	31	generating	generating	NOUN
ejpam-3153	11	32	function[2	function[2	NOUN
ejpam-3153	11	33	]	]	PUNCT
ejpam-3153	11	34	to	to	PART
ejpam-3153	11	35	be	be	AUX
ejpam-3153	11	36	∗corresponding	∗corresponde	VERB
ejpam-3153	11	37	author	author	NOUN
ejpam-3153	11	38	.	.	PUNCT
ejpam-3153	12	1	email	email	NOUN
ejpam-3153	12	2	addresses	address	NOUN
ejpam-3153	12	3	:	:	PUNCT
ejpam-3153	12	4	changl2013@hotmail.com	changl2013@hotmail.com	X
ejpam-3153	12	5	(	(	PUNCT
ejpam-3153	12	6	c.	c.	PROPN
ejpam-3153	12	7	liu	liu	PROPN
ejpam-3153	12	8	)	)	PUNCT
ejpam-3153	12	9	,	,	PUNCT
ejpam-3153	13	1	wuyungw@163.com	wuyungw@163.com	PROPN
ejpam-3153	13	2	(	(	PUNCT
ejpam-3153	13	3	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	13	4	)	)	PUNCT
ejpam-3153	13	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3153	14	1	69	69	NUM
ejpam-3153	15	1	c	c	NOUN
ejpam-3153	15	2	©	©	PROPN
ejpam-3153	15	3	2018	2018	NUM
ejpam-3153	15	4	ejpam	ejpam	VERB
ejpam-3153	15	5	all	all	DET
ejpam-3153	15	6	rights	right	NOUN
ejpam-3153	15	7	reserved	reserve	VERB
ejpam-3153	15	8	.	.	PUNCT
ejpam-3153	16	1	c.	c.	PROPN
ejpam-3153	16	2	liu	liu	PROPN
ejpam-3153	16	3	,	,	PUNCT
ejpam-3153	16	4	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	16	5	/	/	SYM
ejpam-3153	16	6	eur	eur	PROPN
ejpam-3153	16	7	.	.	PUNCT
ejpam-3153	17	1	j.	j.	PROPN
ejpam-3153	17	2	pure	pure	PROPN
ejpam-3153	17	3	appl	appl	PROPN
ejpam-3153	17	4	.	.	PROPN
ejpam-3153	17	5	math	math	PROPN
ejpam-3153	17	6	,	,	PUNCT
ejpam-3153	17	7	11	11	NUM
ejpam-3153	17	8	(	(	PUNCT
ejpam-3153	17	9	1	1	NUM
ejpam-3153	17	10	)	)	PUNCT
ejpam-3153	17	11	(	(	PUNCT
ejpam-3153	17	12	2018	2018	NUM
ejpam-3153	17	13	)	)	PUNCT
ejpam-3153	17	14	,	,	PUNCT
ejpam-3153	17	15	69	69	NUM
ejpam-3153	17	16	-	-	SYM
ejpam-3153	17	17	78	78	NUM
ejpam-3153	17	18	70	70	NUM
ejpam-3153	17	19	(	(	PUNCT
ejpam-3153	17	20	(	(	PUNCT
ejpam-3153	17	21	1	1	NUM
ejpam-3153	17	22	+	+	NUM
ejpam-3153	17	23	ξt)ln(1	ξt)ln(1	NOUN
ejpam-3153	17	24	+	+	CCONJ
ejpam-3153	17	25	ξt	ξt	NOUN
ejpam-3153	17	26	)	)	PUNCT
ejpam-3153	17	27	ξt	ξt	NOUN
ejpam-3153	17	28	)	)	PUNCT
ejpam-3153	17	29	k(1	k(1	NOUN
ejpam-3153	17	30	+	+	CCONJ
ejpam-3153	17	31	ξt)x	ξt)x	PROPN
ejpam-3153	17	32	=	=	SYM
ejpam-3153	17	33	∞∑	∞∑	NUM
ejpam-3153	17	34	n=0	n=0	NUM
ejpam-3153	17	35	d̂	d̂	PROPN
ejpam-3153	17	36	(	(	PUNCT
ejpam-3153	17	37	k	k	NOUN
ejpam-3153	17	38	)	)	PUNCT
ejpam-3153	17	39	n	n	CCONJ
ejpam-3153	17	40	,	,	PUNCT
ejpam-3153	17	41	ξ(x	ξ(x	NOUN
ejpam-3153	17	42	)	)	PUNCT
ejpam-3153	17	43	tn	tn	PROPN
ejpam-3153	17	44	n	n	PROPN
ejpam-3153	17	45	!	!	PUNCT
ejpam-3153	17	46	.	.	PUNCT
ejpam-3153	18	1	(	(	PUNCT
ejpam-3153	18	2	2	2	X
ejpam-3153	18	3	)	)	PUNCT
ejpam-3153	18	4	in	in	ADP
ejpam-3153	18	5	special	special	ADJ
ejpam-3153	18	6	case	case	NOUN
ejpam-3153	18	7	,	,	PUNCT
ejpam-3153	18	8	when	when	SCONJ
ejpam-3153	18	9	x	x	X
ejpam-3153	18	10	=	=	SYM
ejpam-3153	18	11	0	0	NUM
ejpam-3153	18	12	,	,	PUNCT
ejpam-3153	18	13	d̂	d̂	PROPN
ejpam-3153	18	14	(	(	PUNCT
ejpam-3153	18	15	k	k	NOUN
ejpam-3153	18	16	)	)	PUNCT
ejpam-3153	18	17	n	n	CCONJ
ejpam-3153	18	18	,	,	PUNCT
ejpam-3153	18	19	ξ	ξ	X
ejpam-3153	18	20	=	=	SYM
ejpam-3153	18	21	d̂	d̂	PROPN
ejpam-3153	18	22	(	(	PUNCT
ejpam-3153	18	23	k	k	NOUN
ejpam-3153	18	24	)	)	PUNCT
ejpam-3153	18	25	n	n	CCONJ
ejpam-3153	18	26	,	,	PUNCT
ejpam-3153	18	27	ξ(0	ξ(0	NOUN
ejpam-3153	18	28	)	)	PUNCT
ejpam-3153	18	29	are	be	AUX
ejpam-3153	18	30	called	call	VERB
ejpam-3153	18	31	higher	high	ADJ
ejpam-3153	18	32	-	-	PUNCT
ejpam-3153	18	33	order	order	NOUN
ejpam-3153	18	34	twisted	twisted	ADJ
ejpam-3153	18	35	daehee	daehee	NOUN
ejpam-3153	18	36	numbers	number	NOUN
ejpam-3153	18	37	of	of	ADP
ejpam-3153	18	38	the	the	DET
ejpam-3153	18	39	second	second	ADJ
ejpam-3153	18	40	kind	kind	NOUN
ejpam-3153	18	41	.	.	PUNCT
ejpam-3153	19	1	similarly	similarly	ADV
ejpam-3153	19	2	,	,	PUNCT
ejpam-3153	19	3	d̂	d̂	PROPN
ejpam-3153	19	4	(	(	PUNCT
ejpam-3153	19	5	k	k	NOUN
ejpam-3153	19	6	)	)	PUNCT
ejpam-3153	19	7	n	n	NOUN
ejpam-3153	19	8	=	=	SYM
ejpam-3153	19	9	d̂	d̂	PROPN
ejpam-3153	19	10	(	(	PUNCT
ejpam-3153	19	11	k	k	X
ejpam-3153	19	12	)	)	PUNCT
ejpam-3153	19	13	n,1	n,1	NOUN
ejpam-3153	19	14	are	be	AUX
ejpam-3153	19	15	higher	high	ADJ
ejpam-3153	19	16	-	-	PUNCT
ejpam-3153	19	17	order	order	NOUN
ejpam-3153	19	18	daehee	daehee	NOUN
ejpam-3153	19	19	numbers	number	NOUN
ejpam-3153	19	20	of	of	ADP
ejpam-3153	19	21	the	the	DET
ejpam-3153	19	22	second	second	ADJ
ejpam-3153	19	23	kind	kind	NOUN
ejpam-3153	19	24	,	,	PUNCT
ejpam-3153	19	25	d̂n	d̂n	NOUN
ejpam-3153	19	26	,	,	PUNCT
ejpam-3153	19	27	ξ	ξ	X
ejpam-3153	19	28	=	=	SYM
ejpam-3153	19	29	d̂	d̂	X
ejpam-3153	19	30	(	(	PUNCT
ejpam-3153	19	31	1	1	NUM
ejpam-3153	19	32	)	)	PUNCT
ejpam-3153	19	33	n	n	CCONJ
ejpam-3153	19	34	,	,	PUNCT
ejpam-3153	19	35	ξ	ξ	PROPN
ejpam-3153	19	36	are	be	AUX
ejpam-3153	19	37	twisted	twist	VERB
ejpam-3153	19	38	daehee	daehee	NOUN
ejpam-3153	19	39	numbers	number	NOUN
ejpam-3153	19	40	of	of	ADP
ejpam-3153	19	41	the	the	DET
ejpam-3153	19	42	second	second	ADJ
ejpam-3153	19	43	kind	kind	NOUN
ejpam-3153	19	44	,	,	PUNCT
ejpam-3153	19	45	and	and	CCONJ
ejpam-3153	19	46	d̂n	d̂n	X
ejpam-3153	19	47	=	=	SYM
ejpam-3153	19	48	d̂	d̂	X
ejpam-3153	19	49	(	(	PUNCT
ejpam-3153	19	50	1	1	X
ejpam-3153	19	51	)	)	PUNCT
ejpam-3153	19	52	n,1	n,1	NOUN
ejpam-3153	19	53	are	be	AUX
ejpam-3153	19	54	daehee	daehee	NOUN
ejpam-3153	19	55	numbers	number	NOUN
ejpam-3153	19	56	of	of	ADP
ejpam-3153	19	57	the	the	DET
ejpam-3153	19	58	second	second	ADJ
ejpam-3153	19	59	kind	kind	NOUN
ejpam-3153	19	60	.	.	PUNCT
ejpam-3153	20	1	let	let	AUX
ejpam-3153	20	2	ch	ch	NOUN
ejpam-3153	20	3	(	(	PUNCT
ejpam-3153	20	4	r	r	NOUN
ejpam-3153	20	5	)	)	PUNCT
ejpam-3153	20	6	n	n	NOUN
ejpam-3153	20	7	(	(	PUNCT
ejpam-3153	20	8	x	x	X
ejpam-3153	20	9	)	)	PUNCT
ejpam-3153	20	10	denote	denote	VERB
ejpam-3153	20	11	the	the	DET
ejpam-3153	20	12	nth	nth	NOUN
ejpam-3153	20	13	changhee	changhee	NOUN
ejpam-3153	20	14	polynomials	polynomial	NOUN
ejpam-3153	20	15	of	of	ADP
ejpam-3153	20	16	order	order	NOUN
ejpam-3153	20	17	r(∈	r(∈	NOUN
ejpam-3153	20	18	n	n	CCONJ
ejpam-3153	20	19	)	)	PUNCT
ejpam-3153	20	20	,	,	PUNCT
ejpam-3153	20	21	which	which	PRON
ejpam-3153	20	22	are	be	AUX
ejpam-3153	20	23	defined	define	VERB
ejpam-3153	20	24	by	by	ADP
ejpam-3153	20	25	the	the	DET
ejpam-3153	20	26	generating	generating	NOUN
ejpam-3153	20	27	function[1	function[1	PROPN
ejpam-3153	20	28	]	]	PUNCT
ejpam-3153	20	29	to	to	PART
ejpam-3153	20	30	be	be	AUX
ejpam-3153	20	31	(	(	PUNCT
ejpam-3153	20	32	2	2	NUM
ejpam-3153	20	33	2	2	NUM
ejpam-3153	20	34	+	+	NUM
ejpam-3153	20	35	t	t	NOUN
ejpam-3153	20	36	)	)	PUNCT
ejpam-3153	20	37	r(1	r(1	PROPN
ejpam-3153	21	1	+	+	PUNCT
ejpam-3153	21	2	t)x	t)x	NOUN
ejpam-3153	21	3	=	=	PUNCT
ejpam-3153	21	4	∞∑	∞∑	NUM
ejpam-3153	21	5	n=0	n=0	NUM
ejpam-3153	21	6	ch(r	ch(r	NOUN
ejpam-3153	21	7	)	)	PUNCT
ejpam-3153	21	8	n	n	CCONJ
ejpam-3153	21	9	(	(	PUNCT
ejpam-3153	21	10	x	x	X
ejpam-3153	21	11	)	)	PUNCT
ejpam-3153	21	12	tn	tn	PROPN
ejpam-3153	21	13	n	n	NUM
ejpam-3153	21	14	!	!	PUNCT
ejpam-3153	21	15	.	.	PUNCT
ejpam-3153	22	1	(	(	PUNCT
ejpam-3153	22	2	3	3	X
ejpam-3153	22	3	)	)	PUNCT
ejpam-3153	22	4	when	when	SCONJ
ejpam-3153	22	5	x	x	X
ejpam-3153	22	6	=	=	SYM
ejpam-3153	22	7	0	0	NUM
ejpam-3153	22	8	,	,	PUNCT
ejpam-3153	22	9	ch	ch	NOUN
ejpam-3153	22	10	(	(	PUNCT
ejpam-3153	22	11	r	r	NOUN
ejpam-3153	22	12	)	)	PUNCT
ejpam-3153	22	13	n	n	CCONJ
ejpam-3153	22	14	(	(	PUNCT
ejpam-3153	22	15	0	0	NUM
ejpam-3153	22	16	)	)	PUNCT
ejpam-3153	22	17	=	=	SYM
ejpam-3153	22	18	ch	ch	NOUN
ejpam-3153	22	19	(	(	PUNCT
ejpam-3153	22	20	r	r	NOUN
ejpam-3153	22	21	)	)	PUNCT
ejpam-3153	22	22	n	n	NOUN
ejpam-3153	22	23	are	be	AUX
ejpam-3153	22	24	called	call	VERB
ejpam-3153	22	25	higher	high	ADJ
ejpam-3153	22	26	-	-	PUNCT
ejpam-3153	22	27	order	order	NOUN
ejpam-3153	22	28	changhee	changhee	NOUN
ejpam-3153	22	29	numbers	number	NOUN
ejpam-3153	22	30	.	.	PUNCT
ejpam-3153	23	1	let	let	VERB
ejpam-3153	23	2	ĉh	ĉh	NOUN
ejpam-3153	23	3	(	(	PUNCT
ejpam-3153	23	4	r	r	NOUN
ejpam-3153	23	5	)	)	PUNCT
ejpam-3153	23	6	n	n	NOUN
ejpam-3153	23	7	(	(	PUNCT
ejpam-3153	23	8	x	x	X
ejpam-3153	23	9	)	)	PUNCT
ejpam-3153	23	10	denote	denote	VERB
ejpam-3153	23	11	the	the	DET
ejpam-3153	23	12	nth	nth	NOUN
ejpam-3153	23	13	changhee	changhee	NOUN
ejpam-3153	23	14	polynomials	polynomial	NOUN
ejpam-3153	23	15	of	of	ADP
ejpam-3153	23	16	order	order	NOUN
ejpam-3153	23	17	r(∈	r(∈	NOUN
ejpam-3153	23	18	n	n	CCONJ
ejpam-3153	23	19	)	)	PUNCT
ejpam-3153	23	20	of	of	ADP
ejpam-3153	23	21	the	the	DET
ejpam-3153	23	22	second	second	ADJ
ejpam-3153	23	23	kind	kind	NOUN
ejpam-3153	23	24	,	,	PUNCT
ejpam-3153	23	25	which	which	PRON
ejpam-3153	23	26	are	be	AUX
ejpam-3153	23	27	defined	define	VERB
ejpam-3153	23	28	by	by	ADP
ejpam-3153	23	29	the	the	DET
ejpam-3153	23	30	generating	generating	NOUN
ejpam-3153	23	31	function[1	function[1	PROPN
ejpam-3153	23	32	]	]	PUNCT
ejpam-3153	23	33	to	to	PART
ejpam-3153	23	34	be	be	AUX
ejpam-3153	23	35	(	(	PUNCT
ejpam-3153	23	36	2	2	NUM
ejpam-3153	23	37	2	2	NUM
ejpam-3153	23	38	+	+	NUM
ejpam-3153	23	39	t	t	NOUN
ejpam-3153	23	40	)	)	PUNCT
ejpam-3153	23	41	r(1	r(1	PROPN
ejpam-3153	24	1	+	+	NUM
ejpam-3153	24	2	t)x+r	t)x+r	X
ejpam-3153	24	3	=	=	PUNCT
ejpam-3153	25	1	∞∑	∞∑	NUM
ejpam-3153	25	2	n=0	n=0	PROPN
ejpam-3153	25	3	ĉh(r	ĉh(r	NOUN
ejpam-3153	25	4	)	)	PUNCT
ejpam-3153	25	5	n	n	CCONJ
ejpam-3153	25	6	(	(	PUNCT
ejpam-3153	25	7	x	x	X
ejpam-3153	25	8	)	)	PUNCT
ejpam-3153	25	9	tn	tn	PROPN
ejpam-3153	25	10	n	n	NUM
ejpam-3153	25	11	!	!	PUNCT
ejpam-3153	25	12	.	.	PUNCT
ejpam-3153	26	1	(	(	PUNCT
ejpam-3153	26	2	4	4	X
ejpam-3153	26	3	)	)	PUNCT
ejpam-3153	26	4	when	when	SCONJ
ejpam-3153	26	5	x	x	X
ejpam-3153	26	6	=	=	SYM
ejpam-3153	26	7	0	0	NUM
ejpam-3153	26	8	,	,	PUNCT
ejpam-3153	26	9	ĉh	ĉh	NOUN
ejpam-3153	26	10	(	(	PUNCT
ejpam-3153	26	11	r	r	NOUN
ejpam-3153	26	12	)	)	PUNCT
ejpam-3153	26	13	n	n	CCONJ
ejpam-3153	26	14	(	(	PUNCT
ejpam-3153	26	15	0	0	NUM
ejpam-3153	26	16	)	)	PUNCT
ejpam-3153	26	17	=	=	NOUN
ejpam-3153	26	18	ĉh	ĉh	NOUN
ejpam-3153	26	19	(	(	PUNCT
ejpam-3153	26	20	r	r	NOUN
ejpam-3153	26	21	)	)	PUNCT
ejpam-3153	26	22	n	n	NOUN
ejpam-3153	26	23	are	be	AUX
ejpam-3153	26	24	called	call	VERB
ejpam-3153	26	25	higher	high	ADJ
ejpam-3153	26	26	-	-	PUNCT
ejpam-3153	26	27	order	order	NOUN
ejpam-3153	26	28	changhee	changhee	NOUN
ejpam-3153	26	29	numbers	number	NOUN
ejpam-3153	26	30	of	of	ADP
ejpam-3153	26	31	the	the	DET
ejpam-3153	26	32	second	second	ADJ
ejpam-3153	26	33	kind	kind	NOUN
ejpam-3153	26	34	.	.	PUNCT
ejpam-3153	27	1	remark	remark	NOUN
ejpam-3153	27	2	1	1	NUM
ejpam-3153	27	3	.	.	PUNCT
ejpam-3153	28	1	[	[	X
ejpam-3153	28	2	see	see	VERB
ejpam-3153	28	3	7	7	NUM
ejpam-3153	28	4	]	]	PUNCT
ejpam-3153	28	5	if	if	SCONJ
ejpam-3153	28	6	f	f	PROPN
ejpam-3153	28	7	and	and	CCONJ
ejpam-3153	28	8	g	g	PROPN
ejpam-3153	28	9	are	be	AUX
ejpam-3153	28	10	exponential	exponential	ADJ
ejpam-3153	28	11	generating	generating	NOUN
ejpam-3153	28	12	functions	function	NOUN
ejpam-3153	28	13	,	,	PUNCT
ejpam-3153	28	14	and	and	CCONJ
ejpam-3153	28	15	fg	fg	PROPN
ejpam-3153	28	16	=	=	SYM
ejpam-3153	28	17	(	(	PUNCT
ejpam-3153	28	18	∞∑	∞∑	NUM
ejpam-3153	28	19	r=0	r=0	ADJ
ejpam-3153	28	20	arx	arx	PROPN
ejpam-3153	28	21	r	r	NOUN
ejpam-3153	28	22	r	r	NOUN
ejpam-3153	28	23	!	!	PUNCT
ejpam-3153	28	24	)	)	PUNCT
ejpam-3153	29	1	(	(	PUNCT
ejpam-3153	29	2	∞∑	∞∑	NUM
ejpam-3153	29	3	s=0	s=0	X
ejpam-3153	29	4	bsx	bsx	X
ejpam-3153	29	5	s	s	PROPN
ejpam-3153	29	6	s	s	PROPN
ejpam-3153	29	7	!	!	PUNCT
ejpam-3153	29	8	)	)	PUNCT
ejpam-3153	29	9	,	,	PUNCT
ejpam-3153	29	10	then	then	ADV
ejpam-3153	29	11	the	the	DET
ejpam-3153	29	12	coefficients	coefficient	NOUN
ejpam-3153	29	13	of	of	ADP
ejpam-3153	29	14	xn	xn	PROPN
ejpam-3153	29	15	n	n	CCONJ
ejpam-3153	29	16	!	!	PUNCT
ejpam-3153	30	1	in	in	ADP
ejpam-3153	30	2	fg	fg	PROPN
ejpam-3153	30	3	are	be	AUX
ejpam-3153	30	4	given	give	VERB
ejpam-3153	30	5	by	by	ADP
ejpam-3153	30	6	[	[	PUNCT
ejpam-3153	30	7	xn	xn	PROPN
ejpam-3153	30	8	n	n	NUM
ejpam-3153	30	9	!	!	NUM
ejpam-3153	30	10	]	]	PUNCT
ejpam-3153	30	11	(	(	PUNCT
ejpam-3153	30	12	fg	fg	NOUN
ejpam-3153	30	13	)	)	PUNCT
ejpam-3153	30	14	=	=	SYM
ejpam-3153	31	1	n∑	n∑	NOUN
ejpam-3153	31	2	r=0	r=0	PROPN
ejpam-3153	31	3	(	(	PUNCT
ejpam-3153	31	4	n	n	CCONJ
ejpam-3153	31	5	r	r	NOUN
ejpam-3153	31	6	)	)	PUNCT
ejpam-3153	31	7	arbn−r	arbn−r	PROPN
ejpam-3153	31	8	.	.	PUNCT
ejpam-3153	32	1	remark	remark	PROPN
ejpam-3153	32	2	2	2	NUM
ejpam-3153	32	3	.	.	PUNCT
ejpam-3153	33	1	throughout	throughout	ADP
ejpam-3153	33	2	this	this	DET
ejpam-3153	33	3	paper	paper	NOUN
ejpam-3153	33	4	,	,	PUNCT
ejpam-3153	33	5	symbol	symbol	NOUN
ejpam-3153	33	6	e	e	NOUN
ejpam-3153	33	7	denotes	denote	VERB
ejpam-3153	33	8	the	the	DET
ejpam-3153	33	9	expectation	expectation	NOUN
ejpam-3153	33	10	operator	operator	NOUN
ejpam-3153	33	11	defined	define	VERB
ejpam-3153	33	12	by	by	ADP
ejpam-3153	33	13	ef(x	ef(x	NOUN
ejpam-3153	33	14	)	)	PUNCT
ejpam-3153	33	15	=	=	SYM
ejpam-3153	34	1	∫	∫	PROPN
ejpam-3153	35	1	+	+	NUM
ejpam-3153	35	2	∞	∞	PROPN
ejpam-3153	35	3	−∞	−∞	ADP
ejpam-3153	35	4	f(x)p(x)dx	f(x)p(x)dx	NOUN
ejpam-3153	35	5	,	,	PUNCT
ejpam-3153	35	6	where	where	SCONJ
ejpam-3153	35	7	random	random	ADJ
ejpam-3153	35	8	variable	variable	NOUN
ejpam-3153	35	9	x	x	PUNCT
ejpam-3153	35	10	is	be	AUX
ejpam-3153	35	11	continuous	continuous	ADJ
ejpam-3153	35	12	,	,	PUNCT
ejpam-3153	35	13	whose	whose	DET
ejpam-3153	35	14	density	density	NOUN
ejpam-3153	35	15	function	function	NOUN
ejpam-3153	35	16	is	be	AUX
ejpam-3153	35	17	p(x	p(x	PROPN
ejpam-3153	35	18	)	)	PUNCT
ejpam-3153	35	19	.	.	PUNCT
ejpam-3153	36	1	specially	specially	ADV
ejpam-3153	36	2	,	,	PUNCT
ejpam-3153	36	3	when	when	SCONJ
ejpam-3153	36	4	f(x	f(x	PROPN
ejpam-3153	36	5	)	)	PUNCT
ejpam-3153	36	6	=	=	SYM
ejpam-3153	36	7	xn	xn	PROPN
ejpam-3153	36	8	,	,	PUNCT
ejpam-3153	36	9	exn	exn	PROPN
ejpam-3153	36	10	denotes	denote	NOUN
ejpam-3153	36	11	n	n	CCONJ
ejpam-3153	36	12	-	-	PUNCT
ejpam-3153	36	13	order	order	NOUN
ejpam-3153	36	14	moment	moment	NOUN
ejpam-3153	36	15	of	of	ADP
ejpam-3153	36	16	random	random	ADJ
ejpam-3153	36	17	variable	variable	NOUN
ejpam-3153	36	18	x.	x.	NOUN
ejpam-3153	36	19	(	(	PUNCT
ejpam-3153	36	20	i	i	NOUN
ejpam-3153	36	21	)	)	PUNCT
ejpam-3153	36	22	when	when	SCONJ
ejpam-3153	36	23	r.v	r.v	PRON
ejpam-3153	36	24	u	u	NOUN
ejpam-3153	36	25	∼	∼	NOUN
ejpam-3153	36	26	u	u	NOUN
ejpam-3153	36	27	[	[	X
ejpam-3153	36	28	0	0	NUM
ejpam-3153	36	29	,	,	PUNCT
ejpam-3153	36	30	1	1	NUM
ejpam-3153	36	31	]	]	PUNCT
ejpam-3153	36	32	,	,	PUNCT
ejpam-3153	36	33	eun	eun	NOUN
ejpam-3153	36	34	=	=	NOUN
ejpam-3153	36	35	1	1	NUM
ejpam-3153	36	36	n+1	n+1	PROPN
ejpam-3153	36	37	,	,	PUNCT
ejpam-3153	36	38	c.	c.	PROPN
ejpam-3153	36	39	liu	liu	PROPN
ejpam-3153	36	40	,	,	PUNCT
ejpam-3153	36	41	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	36	42	/	/	SYM
ejpam-3153	36	43	eur	eur	PROPN
ejpam-3153	36	44	.	.	PUNCT
ejpam-3153	37	1	j.	j.	PROPN
ejpam-3153	37	2	pure	pure	PROPN
ejpam-3153	37	3	appl	appl	PROPN
ejpam-3153	37	4	.	.	PROPN
ejpam-3153	37	5	math	math	PROPN
ejpam-3153	37	6	,	,	PUNCT
ejpam-3153	37	7	11	11	NUM
ejpam-3153	37	8	(	(	PUNCT
ejpam-3153	37	9	1	1	NUM
ejpam-3153	37	10	)	)	PUNCT
ejpam-3153	37	11	(	(	PUNCT
ejpam-3153	37	12	2018	2018	NUM
ejpam-3153	37	13	)	)	PUNCT
ejpam-3153	37	14	,	,	PUNCT
ejpam-3153	37	15	69	69	NUM
ejpam-3153	37	16	-	-	SYM
ejpam-3153	37	17	78	78	NUM
ejpam-3153	37	18	71	71	NUM
ejpam-3153	37	19	(	(	PUNCT
ejpam-3153	37	20	ii	ii	NOUN
ejpam-3153	37	21	)	)	PUNCT
ejpam-3153	37	22	when	when	SCONJ
ejpam-3153	37	23	r.v	r.v	NOUN
ejpam-3153	37	24	x	x	VERB
ejpam-3153	37	25	∼	∼	NOUN
ejpam-3153	37	26	γ(1	γ(1	PROPN
ejpam-3153	37	27	,	,	PUNCT
ejpam-3153	37	28	1	1	NUM
ejpam-3153	37	29	)	)	PUNCT
ejpam-3153	37	30	,	,	PUNCT
ejpam-3153	37	31	exn	exn	NOUN
ejpam-3153	37	32	=	=	SYM
ejpam-3153	37	33	n	n	X
ejpam-3153	37	34	!	!	PUNCT
ejpam-3153	37	35	.	.	PUNCT
ejpam-3153	38	1	definition	definition	NOUN
ejpam-3153	38	2	1	1	NUM
ejpam-3153	38	3	.	.	PUNCT
ejpam-3153	39	1	the	the	DET
ejpam-3153	39	2	characteristic	characteristic	ADJ
ejpam-3153	39	3	function	function	NOUN
ejpam-3153	39	4	of	of	ADP
ejpam-3153	39	5	random	random	ADJ
ejpam-3153	39	6	variable	variable	NOUN
ejpam-3153	39	7	x	x	PUNCT
ejpam-3153	39	8	is	be	AUX
ejpam-3153	39	9	defined	define	VERB
ejpam-3153	39	10	as	as	ADP
ejpam-3153	39	11	ϕ(t	ϕ(t	NUM
ejpam-3153	39	12	)	)	PUNCT
ejpam-3153	40	1	=	=	SYM
ejpam-3153	40	2	eeitx	eeitx	NOUN
ejpam-3153	40	3	,	,	PUNCT
ejpam-3153	40	4	i2	i2	PROPN
ejpam-3153	40	5	=	=	PROPN
ejpam-3153	40	6	−1,−∞	−1,−∞	PROPN
ejpam-3153	40	7	<	<	X
ejpam-3153	40	8	t	t	PROPN
ejpam-3153	40	9	<	<	X
ejpam-3153	40	10	∞.	∞.	PROPN
ejpam-3153	40	11	(	(	PUNCT
ejpam-3153	40	12	5	5	NUM
ejpam-3153	40	13	)	)	PUNCT
ejpam-3153	40	14	when	when	SCONJ
ejpam-3153	40	15	the	the	DET
ejpam-3153	40	16	moments	moment	NOUN
ejpam-3153	40	17	of	of	ADP
ejpam-3153	40	18	all	all	DET
ejpam-3153	40	19	orders	order	NOUN
ejpam-3153	40	20	of	of	ADP
ejpam-3153	40	21	r.v	r.v	PROPN
ejpam-3153	40	22	.	.	PUNCT
ejpam-3153	40	23	x	x	PUNCT
ejpam-3153	40	24	exist	exist	VERB
ejpam-3153	40	25	,	,	PUNCT
ejpam-3153	40	26	the	the	DET
ejpam-3153	40	27	following	follow	VERB
ejpam-3153	40	28	relation	relation	NOUN
ejpam-3153	40	29	expression	expression	NOUN
ejpam-3153	40	30	holds	hold	VERB
ejpam-3153	40	31	true	true	ADJ
ejpam-3153	40	32	,	,	PUNCT
ejpam-3153	40	33	exn	exn	PROPN
ejpam-3153	40	34	=	=	X
ejpam-3153	40	35	[	[	PUNCT
ejpam-3153	40	36	(	(	PUNCT
ejpam-3153	40	37	it)n	it)n	PROPN
ejpam-3153	40	38	n	n	NUM
ejpam-3153	40	39	!	!	PUNCT
ejpam-3153	41	1	]	]	PUNCT
ejpam-3153	41	2	ϕ(t	ϕ(t	NUM
ejpam-3153	41	3	)	)	PUNCT
ejpam-3153	41	4	,	,	PUNCT
ejpam-3153	41	5	i2	i2	NOUN
ejpam-3153	41	6	=	=	SYM
ejpam-3153	41	7	−1	−1	NOUN
ejpam-3153	41	8	.	.	PUNCT
ejpam-3153	42	1	(	(	PUNCT
ejpam-3153	42	2	6	6	X
ejpam-3153	42	3	)	)	PUNCT
ejpam-3153	42	4	remark	remark	NOUN
ejpam-3153	42	5	3	3	NUM
ejpam-3153	42	6	.	.	PUNCT
ejpam-3153	43	1	[	[	X
ejpam-3153	43	2	see	see	VERB
ejpam-3153	43	3	5	5	NUM
ejpam-3153	43	4	]	]	PUNCT
ejpam-3153	43	5	if	if	SCONJ
ejpam-3153	43	6	random	random	ADJ
ejpam-3153	43	7	variable	variable	NOUN
ejpam-3153	43	8	x	x	PUNCT
ejpam-3153	43	9	is	be	AUX
ejpam-3153	43	10	distributed	distribute	VERB
ejpam-3153	43	11	as	as	ADP
ejpam-3153	43	12	γ(α	γ(α	NOUN
ejpam-3153	43	13	,	,	PUNCT
ejpam-3153	43	14	λ	λ	PROPN
ejpam-3153	43	15	)	)	PUNCT
ejpam-3153	43	16	,	,	PUNCT
ejpam-3153	43	17	where	where	SCONJ
ejpam-3153	43	18	α	α	X
ejpam-3153	43	19	,	,	PUNCT
ejpam-3153	43	20	λ	λ	X
ejpam-3153	43	21	>	>	X
ejpam-3153	43	22	0	0	PROPN
ejpam-3153	43	23	,	,	PUNCT
ejpam-3153	43	24	its	its	PRON
ejpam-3153	43	25	characteristic	characteristic	ADJ
ejpam-3153	43	26	function	function	NOUN
ejpam-3153	43	27	is	be	AUX
ejpam-3153	43	28	ϕ(t	ϕ(t	NUM
ejpam-3153	43	29	)	)	PUNCT
ejpam-3153	44	1	=	=	SYM
ejpam-3153	44	2	eeitx	eeitx	NOUN
ejpam-3153	44	3	=	=	SYM
ejpam-3153	44	4	(	(	PUNCT
ejpam-3153	44	5	1−	1−	NUM
ejpam-3153	44	6	it	it	PRON
ejpam-3153	44	7	λ	λ	NOUN
ejpam-3153	44	8	)	)	PUNCT
ejpam-3153	44	9	−α	−α	NOUN
ejpam-3153	44	10	.	.	PUNCT
ejpam-3153	45	1	(	(	PUNCT
ejpam-3153	45	2	7	7	X
ejpam-3153	45	3	)	)	PUNCT
ejpam-3153	45	4	remark	remark	NOUN
ejpam-3153	45	5	4	4	NUM
ejpam-3153	45	6	.	.	NUM
ejpam-3153	46	1	x	x	PUNCT
ejpam-3153	47	1	and	and	CCONJ
ejpam-3153	47	2	y	y	PROPN
ejpam-3153	47	3	are	be	AUX
ejpam-3153	47	4	two	two	NUM
ejpam-3153	47	5	random	random	ADJ
ejpam-3153	47	6	variables	variable	NOUN
ejpam-3153	47	7	,	,	PUNCT
ejpam-3153	47	8	when	when	SCONJ
ejpam-3153	47	9	cov(x	cov(x	PROPN
ejpam-3153	47	10	,	,	PUNCT
ejpam-3153	47	11	y)=0	y)=0	PROPN
ejpam-3153	47	12	,	,	PUNCT
ejpam-3153	47	13	we	we	PRON
ejpam-3153	47	14	have	have	VERB
ejpam-3153	47	15	e(xy)=ex·ey	e(xy)=ex·ey	NOUN
ejpam-3153	47	16	,	,	PUNCT
ejpam-3153	47	17	where	where	SCONJ
ejpam-3153	47	18	cov(x	cov(x	PROPN
ejpam-3153	47	19	,	,	PUNCT
ejpam-3153	47	20	y	y	PROPN
ejpam-3153	47	21	)	)	PUNCT
ejpam-3153	47	22	=	=	SYM
ejpam-3153	47	23	e(xy	e(xy	PROPN
ejpam-3153	47	24	)	)	PUNCT
ejpam-3153	47	25	−	−	ADP
ejpam-3153	47	26	e(x)e(y	e(x)e(y	ADV
ejpam-3153	47	27	)	)	PUNCT
ejpam-3153	47	28	then	then	ADV
ejpam-3153	47	29	we	we	PRON
ejpam-3153	47	30	give	give	VERB
ejpam-3153	47	31	three	three	NUM
ejpam-3153	47	32	lemmas	lemma	NOUN
ejpam-3153	47	33	to	to	PART
ejpam-3153	47	34	introduce	introduce	VERB
ejpam-3153	47	35	moment	moment	NOUN
ejpam-3153	47	36	representations	representation	NOUN
ejpam-3153	47	37	of	of	ADP
ejpam-3153	47	38	some	some	DET
ejpam-3153	47	39	special	special	ADJ
ejpam-3153	47	40	combinatorial	combinatorial	ADJ
ejpam-3153	47	41	sequences	sequence	NOUN
ejpam-3153	47	42	.	.	PUNCT
ejpam-3153	48	1	lemma	lemma	PROPN
ejpam-3153	48	2	1	1	NUM
ejpam-3153	48	3	.	.	PUNCT
ejpam-3153	49	1	[	[	X
ejpam-3153	49	2	see	see	VERB
ejpam-3153	49	3	6	6	NUM
ejpam-3153	49	4	]	]	PUNCT
ejpam-3153	49	5	assume	assume	VERB
ejpam-3153	49	6	that	that	SCONJ
ejpam-3153	49	7	r.v	r.v	NOUN
ejpam-3153	49	8	x	x	PUNCT
ejpam-3153	49	9	∼	∼	NOUN
ejpam-3153	49	10	γ(u	γ(u	NOUN
ejpam-3153	49	11	,	,	PUNCT
ejpam-3153	49	12	1	1	NUM
ejpam-3153	49	13	)	)	PUNCT
ejpam-3153	49	14	,	,	PUNCT
ejpam-3153	49	15	with	with	ADP
ejpam-3153	49	16	u	u	NOUN
ejpam-3153	49	17	∼	∼	NOUN
ejpam-3153	49	18	u	u	NOUN
ejpam-3153	49	19	[	[	X
ejpam-3153	49	20	0	0	NUM
ejpam-3153	49	21	,	,	PUNCT
ejpam-3153	49	22	1	1	NUM
ejpam-3153	49	23	]	]	PUNCT
ejpam-3153	49	24	is	be	AUX
ejpam-3153	49	25	a	a	DET
ejpam-3153	49	26	random	random	ADJ
ejpam-3153	49	27	variable	variable	NOUN
ejpam-3153	49	28	that	that	PRON
ejpam-3153	49	29	follows	follow	VERB
ejpam-3153	49	30	uniform	uniform	ADJ
ejpam-3153	49	31	distribution	distribution	NOUN
ejpam-3153	49	32	,	,	PUNCT
ejpam-3153	49	33	and	and	CCONJ
ejpam-3153	49	34	x	x	X
ejpam-3153	49	35	,	,	PUNCT
ejpam-3153	49	36	u	u	NOUN
ejpam-3153	49	37	are	be	AUX
ejpam-3153	49	38	independent	independent	ADJ
ejpam-3153	49	39	respectively	respectively	ADV
ejpam-3153	49	40	,	,	PUNCT
ejpam-3153	49	41	then	then	ADV
ejpam-3153	49	42	cauchy	cauchy	NOUN
ejpam-3153	49	43	numbers	number	NOUN
ejpam-3153	49	44	of	of	ADP
ejpam-3153	49	45	the	the	DET
ejpam-3153	49	46	second	second	ADJ
ejpam-3153	49	47	kind	kind	NOUN
ejpam-3153	49	48	ĉn	ĉn	NOUN
ejpam-3153	49	49	,	,	PUNCT
ejpam-3153	49	50	whose	whose	DET
ejpam-3153	49	51	generating	generating	NOUN
ejpam-3153	49	52	function	function	NOUN
ejpam-3153	49	53	is	be	AUX
ejpam-3153	49	54	∞∑	∞∑	NUM
ejpam-3153	49	55	n=0	n=0	NUM
ejpam-3153	49	56	ĉn	ĉn	NUM
ejpam-3153	49	57	xn	xn	NOUN
ejpam-3153	49	58	n	n	X
ejpam-3153	49	59	!	!	PUNCT
ejpam-3153	50	1	=	=	PUNCT
ejpam-3153	50	2	x	x	X
ejpam-3153	50	3	(	(	PUNCT
ejpam-3153	50	4	1	1	NUM
ejpam-3153	50	5	+	+	CCONJ
ejpam-3153	50	6	x	x	X
ejpam-3153	50	7	)	)	PUNCT
ejpam-3153	51	1	ln(1	ln(1	PROPN
ejpam-3153	51	2	+	+	NUM
ejpam-3153	51	3	x	x	X
ejpam-3153	51	4	)	)	PUNCT
ejpam-3153	51	5	,	,	PUNCT
ejpam-3153	51	6	(	(	PUNCT
ejpam-3153	51	7	8)	8)	NUM
ejpam-3153	51	8	have	have	VERB
ejpam-3153	51	9	the	the	DET
ejpam-3153	51	10	following	following	ADJ
ejpam-3153	51	11	moment	moment	NOUN
ejpam-3153	51	12	representation	representation	NOUN
ejpam-3153	51	13	,	,	PUNCT
ejpam-3153	51	14	ĉn	ĉn	PROPN
ejpam-3153	51	15	=	=	SYM
ejpam-3153	51	16	exn	exn	PROPN
ejpam-3153	51	17	,	,	PUNCT
ejpam-3153	51	18	n	n	CCONJ
ejpam-3153	51	19	>	>	X
ejpam-3153	51	20	0	0	NUM
ejpam-3153	51	21	.	.	PUNCT
ejpam-3153	52	1	(	(	PUNCT
ejpam-3153	52	2	9	9	X
ejpam-3153	52	3	)	)	PUNCT
ejpam-3153	52	4	lemma	lemma	PROPN
ejpam-3153	52	5	2	2	NUM
ejpam-3153	52	6	.	.	PUNCT
ejpam-3153	53	1	[	[	AUX
ejpam-3153	53	2	see	see	VERB
ejpam-3153	53	3	6	6	NUM
ejpam-3153	53	4	]	]	PUNCT
ejpam-3153	53	5	assume	assume	VERB
ejpam-3153	53	6	that	that	SCONJ
ejpam-3153	53	7	r.v	r.v	NOUN
ejpam-3153	53	8	x	x	PUNCT
ejpam-3153	53	9	∼	∼	NOUN
ejpam-3153	53	10	γ(1	γ(1	PROPN
ejpam-3153	53	11	,	,	PUNCT
ejpam-3153	53	12	1	1	NUM
ejpam-3153	53	13	)	)	PUNCT
ejpam-3153	53	14	,	,	PUNCT
ejpam-3153	53	15	then	then	ADV
ejpam-3153	53	16	derangement	derangement	NOUN
ejpam-3153	53	17	numbers	number	NOUN
ejpam-3153	53	18	dn	dn	NOUN
ejpam-3153	53	19	=	=	PUNCT
ejpam-3153	53	20	n	n	X
ejpam-3153	53	21	!	!	PUNCT
ejpam-3153	54	1	∑n	∑n	NOUN
ejpam-3153	54	2	k=0	k=0	PROPN
ejpam-3153	54	3	(	(	PUNCT
ejpam-3153	54	4	−1)k	−1)k	PROPN
ejpam-3153	54	5	k	k	AUX
ejpam-3153	54	6	!	!	PROPN
ejpam-3153	54	7	have	have	VERB
ejpam-3153	54	8	the	the	DET
ejpam-3153	54	9	following	following	ADJ
ejpam-3153	54	10	moment	moment	NOUN
ejpam-3153	54	11	representation	representation	NOUN
ejpam-3153	54	12	,	,	PUNCT
ejpam-3153	54	13	dn	dn	NOUN
ejpam-3153	54	14	=	=	PUNCT
ejpam-3153	54	15	e(x	e(x	NUM
ejpam-3153	54	16	−	−	PROPN
ejpam-3153	54	17	1)n	1)n	NUM
ejpam-3153	54	18	,	,	PUNCT
ejpam-3153	54	19	n	n	PROPN
ejpam-3153	54	20	>	>	X
ejpam-3153	54	21	0	0	NUM
ejpam-3153	54	22	.	.	PUNCT
ejpam-3153	55	1	(	(	PUNCT
ejpam-3153	55	2	10	10	NUM
ejpam-3153	55	3	)	)	PUNCT
ejpam-3153	55	4	lemma	lemma	PROPN
ejpam-3153	55	5	3	3	X
ejpam-3153	55	6	.	.	PUNCT
ejpam-3153	56	1	[	[	X
ejpam-3153	56	2	see	see	VERB
ejpam-3153	56	3	6	6	NUM
ejpam-3153	56	4	]	]	PUNCT
ejpam-3153	56	5	suppose	suppose	VERB
ejpam-3153	56	6	that	that	SCONJ
ejpam-3153	56	7	r.v.s	r.v.s	NOUN
ejpam-3153	56	8	u1	u1	NOUN
ejpam-3153	56	9	,	,	PUNCT
ejpam-3153	56	10	u2	u2	NOUN
ejpam-3153	56	11	,	,	PUNCT
ejpam-3153	56	12	·	·	PUNCT
ejpam-3153	56	13	·	·	PUNCT
ejpam-3153	56	14	·	·	PUNCT
ejpam-3153	56	15	,	,	PUNCT
ejpam-3153	56	16	i.i.d	i.i.d	ADP
ejpam-3153	56	17	∼	∼	NOUN
ejpam-3153	56	18	u	u	NOUN
ejpam-3153	56	19	[	[	X
ejpam-3153	56	20	0	0	NUM
ejpam-3153	56	21	,	,	PUNCT
ejpam-3153	56	22	1	1	NUM
ejpam-3153	56	23	]	]	PUNCT
ejpam-3153	56	24	,	,	PUNCT
ejpam-3153	56	25	r.v.s	r.v.s	VERB
ejpam-3153	56	26	γ1,γ2	γ1,γ2	PROPN
ejpam-3153	56	27	,	,	PUNCT
ejpam-3153	56	28	·	·	PUNCT
ejpam-3153	56	29	·	·	PUNCT
ejpam-3153	56	30	·	·	PUNCT
ejpam-3153	56	31	,	,	PUNCT
ejpam-3153	56	32	i.i.d	i.i.d	ADP
ejpam-3153	56	33	∼	∼	NOUN
ejpam-3153	56	34	γ(1	γ(1	PROPN
ejpam-3153	56	35	,	,	PUNCT
ejpam-3153	56	36	1	1	NUM
ejpam-3153	56	37	)	)	PUNCT
ejpam-3153	56	38	,	,	PUNCT
ejpam-3153	56	39	r.v	r.v	INTJ
ejpam-3153	56	40	ui	ui	NOUN
ejpam-3153	56	41	and	and	CCONJ
ejpam-3153	56	42	γj	γj	PROPN
ejpam-3153	56	43	are	be	AUX
ejpam-3153	56	44	independent	independent	ADJ
ejpam-3153	56	45	respectively	respectively	ADV
ejpam-3153	56	46	for	for	ADP
ejpam-3153	56	47	all	all	DET
ejpam-3153	56	48	i	i	PROPN
ejpam-3153	56	49	,	,	PUNCT
ejpam-3153	56	50	j.	j.	PROPN
ejpam-3153	56	51	when	when	SCONJ
ejpam-3153	56	52	n	n	X
ejpam-3153	56	53	,	,	PUNCT
ejpam-3153	56	54	k	k	PROPN
ejpam-3153	56	55	≥	≥	NUM
ejpam-3153	56	56	1	1	NUM
ejpam-3153	56	57	,	,	PUNCT
ejpam-3153	56	58	stirling	stirling	NOUN
ejpam-3153	56	59	numbers	number	NOUN
ejpam-3153	56	60	of	of	ADP
ejpam-3153	56	61	the	the	DET
ejpam-3153	56	62	first	first	ADJ
ejpam-3153	56	63	kind	kind	NOUN
ejpam-3153	56	64	s(n	s(n	PROPN
ejpam-3153	56	65	,	,	PUNCT
ejpam-3153	56	66	k	k	NOUN
ejpam-3153	56	67	)	)	PUNCT
ejpam-3153	56	68	satisfy	satisfy	NOUN
ejpam-3153	56	69	s(n	s(n	PROPN
ejpam-3153	56	70	,	,	PUNCT
ejpam-3153	56	71	k	k	NOUN
ejpam-3153	56	72	)	)	PUNCT
ejpam-3153	56	73	=	=	SYM
ejpam-3153	56	74	(	(	PUNCT
ejpam-3153	56	75	−1)n−k	−1)n−k	X
ejpam-3153	56	76	(	(	PUNCT
ejpam-3153	56	77	n	n	X
ejpam-3153	56	78	k	k	NOUN
ejpam-3153	56	79	)	)	PUNCT
ejpam-3153	57	1	e(u1γ1	e(u1γ1	PROPN
ejpam-3153	57	2	+	+	CCONJ
ejpam-3153	57	3	u2γ2	u2γ2	X
ejpam-3153	57	4	+	+	NUM
ejpam-3153	57	5	·	·	PUNCT
ejpam-3153	57	6	·	·	PUNCT
ejpam-3153	57	7	·	·	PUNCT
ejpam-3153	57	8	+	+	NUM
ejpam-3153	57	9	ukγk	ukγk	ADJ
ejpam-3153	57	10	)	)	PUNCT
ejpam-3153	57	11	n−k	n−k	NOUN
ejpam-3153	57	12	.	.	PUNCT
ejpam-3153	58	1	(	(	PUNCT
ejpam-3153	58	2	11	11	NUM
ejpam-3153	58	3	)	)	PUNCT
ejpam-3153	58	4	it	it	PRON
ejpam-3153	58	5	is	be	AUX
ejpam-3153	58	6	demanded	demand	VERB
ejpam-3153	58	7	that	that	SCONJ
ejpam-3153	58	8	s(n,0)=s(0,k)=0	s(n,0)=s(0,k)=0	NOUN
ejpam-3153	58	9	,	,	PUNCT
ejpam-3153	58	10	s(0,0)=1	s(0,0)=1	PROPN
ejpam-3153	58	11	.	.	PUNCT
ejpam-3153	58	12	c.	c.	PROPN
ejpam-3153	58	13	liu	liu	PROPN
ejpam-3153	58	14	,	,	PUNCT
ejpam-3153	58	15	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	58	16	/	/	SYM
ejpam-3153	58	17	eur	eur	PROPN
ejpam-3153	58	18	.	.	PUNCT
ejpam-3153	59	1	j.	j.	PROPN
ejpam-3153	59	2	pure	pure	PROPN
ejpam-3153	59	3	appl	appl	PROPN
ejpam-3153	59	4	.	.	PROPN
ejpam-3153	59	5	math	math	PROPN
ejpam-3153	59	6	,	,	PUNCT
ejpam-3153	59	7	11	11	NUM
ejpam-3153	59	8	(	(	PUNCT
ejpam-3153	59	9	1	1	NUM
ejpam-3153	59	10	)	)	PUNCT
ejpam-3153	59	11	(	(	PUNCT
ejpam-3153	59	12	2018	2018	NUM
ejpam-3153	59	13	)	)	PUNCT
ejpam-3153	59	14	,	,	PUNCT
ejpam-3153	59	15	69	69	NUM
ejpam-3153	59	16	-	-	SYM
ejpam-3153	59	17	78	78	NUM
ejpam-3153	59	18	72	72	NUM
ejpam-3153	59	19	2	2	NUM
ejpam-3153	59	20	.	.	PUNCT
ejpam-3153	60	1	moment	moment	NOUN
ejpam-3153	60	2	representations	representation	NOUN
ejpam-3153	60	3	of	of	ADP
ejpam-3153	60	4	daehee	daehee	NOUN
ejpam-3153	60	5	and	and	CCONJ
ejpam-3153	60	6	changhee	changhee	VERB
ejpam-3153	60	7	sequences	sequence	NOUN
ejpam-3153	60	8	in	in	ADP
ejpam-3153	60	9	this	this	DET
ejpam-3153	60	10	section	section	NOUN
ejpam-3153	60	11	,	,	PUNCT
ejpam-3153	60	12	we	we	PRON
ejpam-3153	60	13	use	use	VERB
ejpam-3153	60	14	probabilistic	probabilistic	ADJ
ejpam-3153	60	15	method	method	NOUN
ejpam-3153	60	16	to	to	PART
ejpam-3153	60	17	derive	derive	VERB
ejpam-3153	60	18	moment	moment	NOUN
ejpam-3153	60	19	representations	representation	NOUN
ejpam-3153	60	20	about	about	ADP
ejpam-3153	60	21	two	two	NUM
ejpam-3153	60	22	kinds	kind	NOUN
ejpam-3153	60	23	of	of	ADP
ejpam-3153	60	24	higher	high	ADJ
ejpam-3153	60	25	-	-	PUNCT
ejpam-3153	60	26	order	order	NOUN
ejpam-3153	60	27	twisted	twisted	ADJ
ejpam-3153	60	28	daehee	daehee	NOUN
ejpam-3153	60	29	numbers	number	NOUN
ejpam-3153	60	30	and	and	CCONJ
ejpam-3153	60	31	polynomials	polynomial	NOUN
ejpam-3153	60	32	,	,	PUNCT
ejpam-3153	60	33	and	and	CCONJ
ejpam-3153	60	34	two	two	NUM
ejpam-3153	60	35	kinds	kind	NOUN
ejpam-3153	60	36	of	of	ADP
ejpam-3153	60	37	higher	high	ADJ
ejpam-3153	60	38	-	-	PUNCT
ejpam-3153	60	39	order	order	NOUN
ejpam-3153	60	40	changhee	changhee	NOUN
ejpam-3153	60	41	numbers	number	NOUN
ejpam-3153	60	42	and	and	CCONJ
ejpam-3153	60	43	polynomials	polynomial	NOUN
ejpam-3153	60	44	.	.	PUNCT
ejpam-3153	61	1	theorem	theorem	NOUN
ejpam-3153	61	2	1	1	NUM
ejpam-3153	61	3	.	.	PUNCT
ejpam-3153	61	4	assume	assume	VERB
ejpam-3153	61	5	that	that	SCONJ
ejpam-3153	61	6	r.v.s	r.v.s	NOUN
ejpam-3153	61	7	u1	u1	NOUN
ejpam-3153	61	8	,	,	PUNCT
ejpam-3153	61	9	u2	u2	NOUN
ejpam-3153	61	10	,	,	PUNCT
ejpam-3153	61	11	...	...	PUNCT
ejpam-3153	61	12	,	,	PUNCT
ejpam-3153	61	13	i.i.d	i.i.d	ADP
ejpam-3153	61	14	∼	∼	NOUN
ejpam-3153	61	15	u	u	NOUN
ejpam-3153	61	16	[	[	X
ejpam-3153	61	17	0	0	NUM
ejpam-3153	61	18	,	,	PUNCT
ejpam-3153	61	19	1	1	NUM
ejpam-3153	61	20	]	]	PUNCT
ejpam-3153	61	21	,	,	PUNCT
ejpam-3153	61	22	γ1,γ2	γ1,γ2	PROPN
ejpam-3153	61	23	,	,	PUNCT
ejpam-3153	61	24	...	...	PUNCT
ejpam-3153	61	25	,	,	PUNCT
ejpam-3153	61	26	i.i.d	i.i.d	ADP
ejpam-3153	61	27	∼	∼	NOUN
ejpam-3153	61	28	γ(1	γ(1	PROPN
ejpam-3153	61	29	,	,	PUNCT
ejpam-3153	61	30	1	1	NUM
ejpam-3153	61	31	)	)	PUNCT
ejpam-3153	61	32	,	,	PUNCT
ejpam-3153	61	33	and	and	CCONJ
ejpam-3153	61	34	for	for	ADP
ejpam-3153	61	35	all	all	DET
ejpam-3153	61	36	i	i	PROPN
ejpam-3153	61	37	,	,	PUNCT
ejpam-3153	61	38	j	j	PROPN
ejpam-3153	61	39	,	,	PUNCT
ejpam-3153	61	40	r.v	r.v	PROPN
ejpam-3153	61	41	ui	ui	NOUN
ejpam-3153	61	42	and	and	CCONJ
ejpam-3153	61	43	γj	γj	PROPN
ejpam-3153	61	44	are	be	AUX
ejpam-3153	61	45	independent	independent	ADJ
ejpam-3153	61	46	.	.	PUNCT
ejpam-3153	62	1	when	when	SCONJ
ejpam-3153	62	2	n	n	X
ejpam-3153	62	3	,	,	PUNCT
ejpam-3153	62	4	m−	m−	PROPN
ejpam-3153	62	5	k	k	PROPN
ejpam-3153	62	6	∈	∈	PROPN
ejpam-3153	62	7	z>0	z>0	PROPN
ejpam-3153	62	8	,	,	PUNCT
ejpam-3153	62	9	k	k	PROPN
ejpam-3153	62	10	∈	∈	PROPN
ejpam-3153	62	11	n	n	CCONJ
ejpam-3153	62	12	,	,	PUNCT
ejpam-3153	62	13	we	we	PRON
ejpam-3153	62	14	have	have	VERB
ejpam-3153	62	15	d	d	NOUN
ejpam-3153	62	16	(	(	PUNCT
ejpam-3153	62	17	k	k	NOUN
ejpam-3153	62	18	)	)	PUNCT
ejpam-3153	62	19	n	n	CCONJ
ejpam-3153	62	20	,	,	PUNCT
ejpam-3153	62	21	ξ	ξ	X
ejpam-3153	62	22	=	=	SYM
ejpam-3153	62	23	(	(	PUNCT
ejpam-3153	62	24	−ξ)ne(u1γ1	−ξ)ne(u1γ1	NOUN
ejpam-3153	63	1	+	+	CCONJ
ejpam-3153	63	2	u2γ2	u2γ2	PUNCT
ejpam-3153	63	3	+	+	NUM
ejpam-3153	63	4	·	·	PUNCT
ejpam-3153	63	5	·	·	PUNCT
ejpam-3153	63	6	·	·	PUNCT
ejpam-3153	63	7	+	+	NUM
ejpam-3153	63	8	ukγk	ukγk	NOUN
ejpam-3153	63	9	)	)	PUNCT
ejpam-3153	63	10	n	n	CCONJ
ejpam-3153	63	11	,	,	PUNCT
ejpam-3153	63	12	(	(	PUNCT
ejpam-3153	63	13	12	12	NUM
ejpam-3153	63	14	)	)	PUNCT
ejpam-3153	63	15	d	d	NOUN
ejpam-3153	63	16	(	(	PUNCT
ejpam-3153	63	17	k	k	NOUN
ejpam-3153	63	18	)	)	PUNCT
ejpam-3153	63	19	m−k	m−k	NOUN
ejpam-3153	63	20	,	,	PUNCT
ejpam-3153	63	21	ξ	ξ	X
ejpam-3153	63	22	=	=	SYM
ejpam-3153	63	23	(	(	PUNCT
ejpam-3153	63	24	−ξ)m−k	−ξ)m−k	NOUN
ejpam-3153	63	25	k	k	NOUN
ejpam-3153	63	26	m	m	VERB
ejpam-3153	63	27	e(u1γ1	e(u1γ1	PROPN
ejpam-3153	63	28	+	+	CCONJ
ejpam-3153	63	29	·	·	PUNCT
ejpam-3153	63	30	·	·	PUNCT
ejpam-3153	63	31	·	·	PUNCT
ejpam-3153	64	1	+	+	CCONJ
ejpam-3153	64	2	uk−1γk−1	uk−1γk−1	PROPN
ejpam-3153	64	3	+	+	NUM
ejpam-3153	64	4	γk	γk	NOUN
ejpam-3153	64	5	)	)	PUNCT
ejpam-3153	64	6	m−k	m−k	NOUN
ejpam-3153	64	7	.	.	PUNCT
ejpam-3153	65	1	(	(	PUNCT
ejpam-3153	65	2	13	13	NUM
ejpam-3153	65	3	)	)	PUNCT
ejpam-3153	65	4	proof	proof	NOUN
ejpam-3153	65	5	.	.	PUNCT
ejpam-3153	66	1	the	the	DET
ejpam-3153	66	2	generating	generate	VERB
ejpam-3153	66	3	function	function	NOUN
ejpam-3153	66	4	of	of	ADP
ejpam-3153	66	5	higher	high	ADJ
ejpam-3153	66	6	-	-	PUNCT
ejpam-3153	66	7	order	order	NOUN
ejpam-3153	66	8	twisted	twisted	ADJ
ejpam-3153	66	9	daehee	daehee	NOUN
ejpam-3153	66	10	numbers	number	NOUN
ejpam-3153	66	11	is	be	AUX
ejpam-3153	66	12	known	know	VERB
ejpam-3153	66	13	as	as	ADP
ejpam-3153	66	14	∞∑	∞∑	NUM
ejpam-3153	66	15	n=0	n=0	NUM
ejpam-3153	66	16	d	d	NOUN
ejpam-3153	66	17	(	(	PUNCT
ejpam-3153	66	18	k	k	NOUN
ejpam-3153	66	19	)	)	PUNCT
ejpam-3153	66	20	n	n	CCONJ
ejpam-3153	66	21	,	,	PUNCT
ejpam-3153	66	22	ξ	ξ	PROPN
ejpam-3153	66	23	tn	tn	PROPN
ejpam-3153	66	24	n	n	X
ejpam-3153	66	25	!	!	PUNCT
ejpam-3153	67	1	=	=	PUNCT
ejpam-3153	68	1	(	(	PUNCT
ejpam-3153	68	2	ln(1	ln(1	NOUN
ejpam-3153	68	3	+	+	NUM
ejpam-3153	68	4	ξt	ξt	X
ejpam-3153	68	5	)	)	PUNCT
ejpam-3153	68	6	ξt	ξt	NOUN
ejpam-3153	68	7	)	)	PUNCT
ejpam-3153	68	8	k	k	NOUN
ejpam-3153	68	9	,	,	PUNCT
ejpam-3153	68	10	(	(	PUNCT
ejpam-3153	68	11	14	14	X
ejpam-3153	68	12	)	)	PUNCT
ejpam-3153	68	13	taking	take	VERB
ejpam-3153	68	14	the	the	DET
ejpam-3153	68	15	coefficients	coefficient	NOUN
ejpam-3153	68	16	of	of	ADP
ejpam-3153	68	17	tn	tn	NOUN
ejpam-3153	68	18	in	in	ADP
ejpam-3153	68	19	the	the	DET
ejpam-3153	68	20	left	left	ADJ
ejpam-3153	68	21	-	-	PUNCT
ejpam-3153	68	22	hand	hand	NOUN
ejpam-3153	68	23	side	side	NOUN
ejpam-3153	68	24	of	of	ADP
ejpam-3153	68	25	eq.(14	eq.(14	NOUN
ejpam-3153	68	26	)	)	PUNCT
ejpam-3153	68	27	,	,	PUNCT
ejpam-3153	68	28	we	we	PRON
ejpam-3153	68	29	get	get	VERB
ejpam-3153	68	30	d	d	X
ejpam-3153	68	31	(	(	PUNCT
ejpam-3153	68	32	k	k	NOUN
ejpam-3153	68	33	)	)	PUNCT
ejpam-3153	68	34	n	n	CCONJ
ejpam-3153	68	35	,	,	PUNCT
ejpam-3153	68	36	ξ	ξ	PROPN
ejpam-3153	68	37	n	n	X
ejpam-3153	68	38	!	!	PUNCT
ejpam-3153	69	1	=	=	PUNCT
ejpam-3153	70	1	[	[	X
ejpam-3153	70	2	tn	tn	X
ejpam-3153	70	3	]	]	X
ejpam-3153	70	4	(	(	PUNCT
ejpam-3153	70	5	ln(1	ln(1	PROPN
ejpam-3153	70	6	+	+	NUM
ejpam-3153	70	7	ξt	ξt	X
ejpam-3153	70	8	)	)	PUNCT
ejpam-3153	70	9	ξt	ξt	NOUN
ejpam-3153	70	10	)	)	PUNCT
ejpam-3153	70	11	k	k	X
ejpam-3153	71	1	=	=	PUNCT
ejpam-3153	72	1	[	[	X
ejpam-3153	72	2	(	(	PUNCT
ejpam-3153	72	3	−t)n	−t)n	NOUN
ejpam-3153	72	4	]	]	X
ejpam-3153	72	5	(	(	PUNCT
ejpam-3153	72	6	∑	∑	PUNCT
ejpam-3153	72	7	i>0	i>0	PROPN
ejpam-3153	72	8	(	(	PUNCT
ejpam-3153	72	9	ξt)i	ξt)i	PROPN
ejpam-3153	72	10	i+	i+	NOUN
ejpam-3153	72	11	1	1	NUM
ejpam-3153	72	12	)	)	PUNCT
ejpam-3153	72	13	k	k	NOUN
ejpam-3153	72	14	=	=	PUNCT
ejpam-3153	73	1	[	[	X
ejpam-3153	73	2	(	(	PUNCT
ejpam-3153	73	3	−t)n	−t)n	NOUN
ejpam-3153	73	4	]	]	X
ejpam-3153	73	5	(	(	PUNCT
ejpam-3153	73	6	∑	∑	PUNCT
ejpam-3153	73	7	i>0	i>0	PROPN
ejpam-3153	73	8	tie(ξu)i)k	tie(ξu)i)k	NOUN
ejpam-3153	73	9	,	,	PUNCT
ejpam-3153	73	10	(	(	PUNCT
ejpam-3153	73	11	15	15	NUM
ejpam-3153	73	12	)	)	PUNCT
ejpam-3153	73	13	(	(	PUNCT
ejpam-3153	73	14	∑	∑	PUNCT
ejpam-3153	73	15	i>0	i>0	PROPN
ejpam-3153	73	16	tie(ξu)i)k	tie(ξu)i)k	NOUN
ejpam-3153	73	17	=	=	PUNCT
ejpam-3153	74	1	∞∑	∞∑	NUM
ejpam-3153	74	2	n=0	n=0	NUM
ejpam-3153	74	3	∑	∑	NOUN
ejpam-3153	74	4	i1+···+ik	i1+···+ik	NOUN
ejpam-3153	74	5	=	=	SYM
ejpam-3153	74	6	n	n	X
ejpam-3153	74	7	(	(	PUNCT
ejpam-3153	74	8	e(ξu1)i1	e(ξu1)i1	PROPN
ejpam-3153	74	9	)	)	PUNCT
ejpam-3153	74	10	·	·	PUNCT
ejpam-3153	74	11	·	·	PUNCT
ejpam-3153	74	12	·	·	PUNCT
ejpam-3153	74	13	(	(	PUNCT
ejpam-3153	74	14	e(ξuk	e(ξuk	X
ejpam-3153	74	15	)	)	PUNCT
ejpam-3153	74	16	ik)tn	ik)tn	PRON
ejpam-3153	75	1	=	=	PUNCT
ejpam-3153	76	1	∞∑	∞∑	ADJ
ejpam-3153	76	2	n=0	n=0	NUM
ejpam-3153	76	3	1	1	NUM
ejpam-3153	76	4	n	n	NOUN
ejpam-3153	76	5	!	!	PUNCT
ejpam-3153	76	6	∑	∑	PUNCT
ejpam-3153	76	7	i1+···+ik	i1+···+ik	NOUN
ejpam-3153	76	8	=	=	SYM
ejpam-3153	76	9	n	n	X
ejpam-3153	76	10	(	(	PUNCT
ejpam-3153	76	11	n	n	X
ejpam-3153	76	12	i1	i1	PROPN
ejpam-3153	76	13	,	,	PUNCT
ejpam-3153	76	14	i2	i2	PROPN
ejpam-3153	76	15	,	,	PUNCT
ejpam-3153	76	16	·	·	PUNCT
ejpam-3153	76	17	·	·	PUNCT
ejpam-3153	76	18	·	·	PUNCT
ejpam-3153	76	19	ik	ik	X
ejpam-3153	76	20	)	)	PUNCT
ejpam-3153	76	21	(	(	PUNCT
ejpam-3153	76	22	e(ξu1)i1	e(ξu1)i1	PROPN
ejpam-3153	76	23	)	)	PUNCT
ejpam-3153	76	24	·	·	PUNCT
ejpam-3153	76	25	·	·	PUNCT
ejpam-3153	76	26	·	·	PUNCT
ejpam-3153	76	27	(	(	PUNCT
ejpam-3153	76	28	e(ξuk	e(ξuk	PROPN
ejpam-3153	76	29	)	)	PUNCT
ejpam-3153	76	30	ik)(i1	ik)(i1	NOUN
ejpam-3153	76	31	!	!	PUNCT
ejpam-3153	76	32	)	)	PUNCT
ejpam-3153	76	33	·	·	PUNCT
ejpam-3153	76	34	·	·	PUNCT
ejpam-3153	76	35	·	·	PUNCT
ejpam-3153	77	1	(	(	PUNCT
ejpam-3153	77	2	ik!)tn	ik!)tn	NOUN
ejpam-3153	77	3	=	=	PUNCT
ejpam-3153	78	1	∞∑	∞∑	PRON
ejpam-3153	78	2	n=0	n=0	NUM
ejpam-3153	78	3	1	1	NUM
ejpam-3153	78	4	n	n	NOUN
ejpam-3153	78	5	!	!	PUNCT
ejpam-3153	78	6	∑	∑	PUNCT
ejpam-3153	78	7	i1+···+ik	i1+···+ik	NOUN
ejpam-3153	78	8	=	=	SYM
ejpam-3153	78	9	n	n	X
ejpam-3153	78	10	(	(	PUNCT
ejpam-3153	78	11	n	n	X
ejpam-3153	78	12	i1	i1	PROPN
ejpam-3153	78	13	,	,	PUNCT
ejpam-3153	78	14	i2	i2	PROPN
ejpam-3153	78	15	,	,	PUNCT
ejpam-3153	78	16	·	·	PUNCT
ejpam-3153	78	17	·	·	PUNCT
ejpam-3153	78	18	·	·	PUNCT
ejpam-3153	78	19	ik	ik	X
ejpam-3153	78	20	)	)	PUNCT
ejpam-3153	78	21	(	(	PUNCT
ejpam-3153	78	22	e(ξu1)i1	e(ξu1)i1	PROPN
ejpam-3153	78	23	)	)	PUNCT
ejpam-3153	78	24	·	·	PUNCT
ejpam-3153	78	25	·	·	PUNCT
ejpam-3153	78	26	·	·	PUNCT
ejpam-3153	78	27	(	(	PUNCT
ejpam-3153	78	28	e(ξuk	e(ξuk	PROPN
ejpam-3153	78	29	)	)	PUNCT
ejpam-3153	78	30	ik)(eγi11	ik)(eγi11	NOUN
ejpam-3153	78	31	)	)	PUNCT
ejpam-3153	78	32	·	·	PUNCT
ejpam-3153	78	33	·	·	PUNCT
ejpam-3153	78	34	·	·	PUNCT
ejpam-3153	78	35	(	(	PUNCT
ejpam-3153	78	36	eγikk	eγikk	PROPN
ejpam-3153	78	37	)	)	PUNCT
ejpam-3153	78	38	tn	tn	NOUN
ejpam-3153	79	1	=	=	PUNCT
ejpam-3153	79	2	∞∑	∞∑	NUM
ejpam-3153	79	3	n=0	n=0	NUM
ejpam-3153	79	4	ξn	ξn	NOUN
ejpam-3153	79	5	n	n	X
ejpam-3153	79	6	!	!	PUNCT
ejpam-3153	80	1	e	e	X
ejpam-3153	80	2	[	[	PUNCT
ejpam-3153	80	3	∑	∑	INTJ
ejpam-3153	80	4	i1+···+ik	i1+···+ik	NOUN
ejpam-3153	80	5	=	=	SYM
ejpam-3153	80	6	n	n	X
ejpam-3153	80	7	(	(	PUNCT
ejpam-3153	80	8	n	n	X
ejpam-3153	80	9	i1	i1	PROPN
ejpam-3153	80	10	,	,	PUNCT
ejpam-3153	80	11	i2	i2	PROPN
ejpam-3153	80	12	,	,	PUNCT
ejpam-3153	80	13	·	·	PUNCT
ejpam-3153	80	14	·	·	PUNCT
ejpam-3153	80	15	·	·	PUNCT
ejpam-3153	80	16	ik	ik	X
ejpam-3153	80	17	)	)	PUNCT
ejpam-3153	80	18	(	(	PUNCT
ejpam-3153	80	19	u1γ1)i1	u1γ1)i1	X
ejpam-3153	80	20	·	·	PUNCT
ejpam-3153	80	21	·	·	PUNCT
ejpam-3153	80	22	·	·	PUNCT
ejpam-3153	80	23	(	(	PUNCT
ejpam-3153	80	24	ukγk)ik	ukγk)ik	ADJ
ejpam-3153	80	25	]	]	X
ejpam-3153	80	26	tn	tn	X
ejpam-3153	81	1	=	=	SYM
ejpam-3153	82	1	∞∑	∞∑	NUM
ejpam-3153	82	2	n=0	n=0	NUM
ejpam-3153	82	3	ξn	ξn	NOUN
ejpam-3153	82	4	n	n	NOUN
ejpam-3153	82	5	!	!	PUNCT
ejpam-3153	83	1	e(u1γ1	e(u1γ1	PROPN
ejpam-3153	83	2	+	+	CCONJ
ejpam-3153	83	3	·	·	PUNCT
ejpam-3153	83	4	·	·	PUNCT
ejpam-3153	83	5	·	·	PUNCT
ejpam-3153	83	6	+	+	NUM
ejpam-3153	83	7	ukγk	ukγk	ADJ
ejpam-3153	83	8	)	)	PUNCT
ejpam-3153	83	9	ntn	ntn	NOUN
ejpam-3153	83	10	.	.	PUNCT
ejpam-3153	84	1	(	(	PUNCT
ejpam-3153	84	2	16	16	NUM
ejpam-3153	84	3	)	)	PUNCT
ejpam-3153	84	4	from	from	ADP
ejpam-3153	84	5	eq.(15	eq.(15	NOUN
ejpam-3153	84	6	)	)	PUNCT
ejpam-3153	84	7	and	and	CCONJ
ejpam-3153	84	8	eq.(16	eq.(16	NOUN
ejpam-3153	84	9	)	)	PUNCT
ejpam-3153	84	10	,	,	PUNCT
ejpam-3153	84	11	we	we	PRON
ejpam-3153	84	12	can	can	AUX
ejpam-3153	84	13	see	see	VERB
ejpam-3153	84	14	that	that	SCONJ
ejpam-3153	85	1	d	d	PROPN
ejpam-3153	85	2	(	(	PUNCT
ejpam-3153	85	3	k	k	NOUN
ejpam-3153	85	4	)	)	PUNCT
ejpam-3153	85	5	n	n	CCONJ
ejpam-3153	85	6	,	,	PUNCT
ejpam-3153	85	7	ξ	ξ	PROPN
ejpam-3153	85	8	n	n	X
ejpam-3153	85	9	!	!	PUNCT
ejpam-3153	85	10	=	=	PUNCT
ejpam-3153	85	11	(	(	PUNCT
ejpam-3153	85	12	−ξ)n	−ξ)n	NOUN
ejpam-3153	85	13	n	n	NOUN
ejpam-3153	85	14	!	!	PUNCT
ejpam-3153	86	1	e(u1γ1	e(u1γ1	VERB
ejpam-3153	86	2	+	+	CCONJ
ejpam-3153	86	3	·	·	PUNCT
ejpam-3153	86	4	·	·	PUNCT
ejpam-3153	86	5	·	·	PUNCT
ejpam-3153	86	6	+	+	NUM
ejpam-3153	86	7	ukγk	ukγk	NOUN
ejpam-3153	86	8	)	)	PUNCT
ejpam-3153	86	9	n	n	CCONJ
ejpam-3153	86	10	,	,	PUNCT
ejpam-3153	86	11	thus	thus	ADV
ejpam-3153	86	12	we	we	PRON
ejpam-3153	86	13	have	have	VERB
ejpam-3153	86	14	d	d	NOUN
ejpam-3153	86	15	(	(	PUNCT
ejpam-3153	86	16	k	k	NOUN
ejpam-3153	86	17	)	)	PUNCT
ejpam-3153	86	18	n	n	CCONJ
ejpam-3153	86	19	,	,	PUNCT
ejpam-3153	86	20	ξ	ξ	X
ejpam-3153	86	21	=	=	SYM
ejpam-3153	86	22	(	(	PUNCT
ejpam-3153	86	23	−ξ)ne(u1γ1	−ξ)ne(u1γ1	NOUN
ejpam-3153	86	24	+	+	X
ejpam-3153	86	25	·	·	PUNCT
ejpam-3153	86	26	·	·	PUNCT
ejpam-3153	86	27	·	·	PUNCT
ejpam-3153	86	28	+	+	NUM
ejpam-3153	86	29	ukγk	ukγk	ADJ
ejpam-3153	86	30	)	)	PUNCT
ejpam-3153	86	31	n.	n.	PROPN
ejpam-3153	86	32	c.	c.	PROPN
ejpam-3153	86	33	liu	liu	PROPN
ejpam-3153	86	34	,	,	PUNCT
ejpam-3153	86	35	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	86	36	/	/	SYM
ejpam-3153	86	37	eur	eur	PROPN
ejpam-3153	86	38	.	.	PUNCT
ejpam-3153	87	1	j.	j.	PROPN
ejpam-3153	87	2	pure	pure	PROPN
ejpam-3153	87	3	appl	appl	PROPN
ejpam-3153	87	4	.	.	PROPN
ejpam-3153	87	5	math	math	PROPN
ejpam-3153	87	6	,	,	PUNCT
ejpam-3153	87	7	11	11	NUM
ejpam-3153	87	8	(	(	PUNCT
ejpam-3153	87	9	1	1	NUM
ejpam-3153	87	10	)	)	PUNCT
ejpam-3153	87	11	(	(	PUNCT
ejpam-3153	87	12	2018	2018	NUM
ejpam-3153	87	13	)	)	PUNCT
ejpam-3153	87	14	,	,	PUNCT
ejpam-3153	87	15	69	69	NUM
ejpam-3153	87	16	-	-	SYM
ejpam-3153	87	17	78	78	NUM
ejpam-3153	87	18	73	73	NUM
ejpam-3153	87	19	eq.(13	eq.(13	NOUN
ejpam-3153	87	20	)	)	PUNCT
ejpam-3153	87	21	can	can	AUX
ejpam-3153	87	22	be	be	AUX
ejpam-3153	87	23	proved	prove	VERB
ejpam-3153	87	24	by	by	ADP
ejpam-3153	87	25	the	the	DET
ejpam-3153	87	26	following	follow	VERB
ejpam-3153	87	27	equation[see	equation[see	VERB
ejpam-3153	87	28	6	6	NUM
ejpam-3153	87	29	]	]	X
ejpam-3153	87	30	e(u1γ1	e(u1γ1	PROPN
ejpam-3153	87	31	+	+	CCONJ
ejpam-3153	87	32	u2γ2	u2γ2	X
ejpam-3153	88	1	+	+	NUM
ejpam-3153	88	2	·	·	PUNCT
ejpam-3153	88	3	·	·	PUNCT
ejpam-3153	88	4	·	·	PUNCT
ejpam-3153	88	5	+	+	NUM
ejpam-3153	88	6	ukγk	ukγk	ADJ
ejpam-3153	88	7	)	)	PUNCT
ejpam-3153	88	8	m−k	m−k	NOUN
ejpam-3153	89	1	=	=	PUNCT
ejpam-3153	89	2	k	k	NOUN
ejpam-3153	89	3	m	m	VERB
ejpam-3153	89	4	e(u1γ1	e(u1γ1	PROPN
ejpam-3153	89	5	+	+	CCONJ
ejpam-3153	89	6	·	·	PUNCT
ejpam-3153	89	7	·	·	PUNCT
ejpam-3153	89	8	·	·	PUNCT
ejpam-3153	89	9	+	+	CCONJ
ejpam-3153	89	10	uk−1γk−1	uk−1γk−1	PROPN
ejpam-3153	89	11	+	+	NUM
ejpam-3153	89	12	γk	γk	NOUN
ejpam-3153	89	13	)	)	PUNCT
ejpam-3153	89	14	m−k	m−k	NOUN
ejpam-3153	89	15	(	(	PUNCT
ejpam-3153	89	16	17	17	NUM
ejpam-3153	89	17	)	)	PUNCT
ejpam-3153	89	18	corollary	corollary	ADJ
ejpam-3153	89	19	1	1	NUM
ejpam-3153	89	20	.	.	PUNCT
ejpam-3153	89	21	in	in	ADP
ejpam-3153	89	22	theorem	theorem	NOUN
ejpam-3153	89	23	1	1	NUM
ejpam-3153	89	24	,	,	PUNCT
ejpam-3153	89	25	when	when	SCONJ
ejpam-3153	89	26	ξ	ξ	X
ejpam-3153	89	27	=	=	SYM
ejpam-3153	89	28	1	1	NUM
ejpam-3153	89	29	,	,	PUNCT
ejpam-3153	89	30	we	we	PRON
ejpam-3153	89	31	obtain	obtain	VERB
ejpam-3153	89	32	the	the	DET
ejpam-3153	89	33	moment	moment	NOUN
ejpam-3153	89	34	representation	representation	NOUN
ejpam-3153	89	35	of	of	ADP
ejpam-3153	89	36	higherorder	higherorder	NOUN
ejpam-3153	89	37	daehee	daehee	NOUN
ejpam-3153	89	38	numbers[3	numbers[3	PROPN
ejpam-3153	89	39	]	]	X
ejpam-3153	89	40	d(k	d(k	PROPN
ejpam-3153	89	41	)	)	PUNCT
ejpam-3153	89	42	n	n	NOUN
ejpam-3153	89	43	=	=	PUNCT
ejpam-3153	89	44	(	(	PUNCT
ejpam-3153	89	45	−1)ne(u1γ1	−1)ne(u1γ1	NOUN
ejpam-3153	89	46	+	+	CCONJ
ejpam-3153	89	47	·	·	PUNCT
ejpam-3153	89	48	·	·	PUNCT
ejpam-3153	89	49	·	·	PUNCT
ejpam-3153	89	50	+	+	NUM
ejpam-3153	89	51	ukγk	ukγk	ADJ
ejpam-3153	89	52	)	)	PUNCT
ejpam-3153	89	53	n.	n.	NOUN
ejpam-3153	89	54	(	(	PUNCT
ejpam-3153	89	55	18	18	NUM
ejpam-3153	89	56	)	)	PUNCT
ejpam-3153	89	57	corollary	corollary	ADJ
ejpam-3153	89	58	2	2	NUM
ejpam-3153	89	59	.	.	PUNCT
ejpam-3153	89	60	in	in	ADP
ejpam-3153	89	61	theorem	theorem	NOUN
ejpam-3153	89	62	1	1	NUM
ejpam-3153	89	63	,	,	PUNCT
ejpam-3153	89	64	when	when	SCONJ
ejpam-3153	89	65	k	k	PROPN
ejpam-3153	89	66	=	=	SYM
ejpam-3153	89	67	1	1	NUM
ejpam-3153	89	68	,	,	PUNCT
ejpam-3153	89	69	we	we	PRON
ejpam-3153	89	70	obtain	obtain	VERB
ejpam-3153	89	71	the	the	DET
ejpam-3153	89	72	moment	moment	NOUN
ejpam-3153	89	73	representation	representation	NOUN
ejpam-3153	89	74	of	of	ADP
ejpam-3153	89	75	twisted	twisted	ADJ
ejpam-3153	89	76	daehee	daehee	NOUN
ejpam-3153	89	77	numbers[2	numbers[2	PROPN
ejpam-3153	89	78	]	]	X
ejpam-3153	89	79	dn	dn	PROPN
ejpam-3153	89	80	,	,	PUNCT
ejpam-3153	89	81	ξ	ξ	X
ejpam-3153	89	82	=	=	SYM
ejpam-3153	89	83	(	(	PUNCT
ejpam-3153	89	84	−ξ)ne(uγ)n	−ξ)ne(uγ)n	NOUN
ejpam-3153	89	85	.	.	PUNCT
ejpam-3153	90	1	(	(	PUNCT
ejpam-3153	90	2	19	19	NUM
ejpam-3153	90	3	)	)	PUNCT
ejpam-3153	90	4	corollary	corollary	ADJ
ejpam-3153	90	5	3	3	NUM
ejpam-3153	90	6	.	.	PUNCT
ejpam-3153	91	1	in	in	ADP
ejpam-3153	91	2	theorem1	theorem1	PROPN
ejpam-3153	91	3	,	,	PUNCT
ejpam-3153	92	1	when	when	SCONJ
ejpam-3153	92	2	ξ	ξ	X
ejpam-3153	92	3	=	=	SYM
ejpam-3153	92	4	1	1	NUM
ejpam-3153	92	5	,	,	PUNCT
ejpam-3153	92	6	k	k	NOUN
ejpam-3153	92	7	=	=	SYM
ejpam-3153	92	8	1	1	NUM
ejpam-3153	92	9	,	,	PUNCT
ejpam-3153	92	10	we	we	PRON
ejpam-3153	92	11	obtain	obtain	VERB
ejpam-3153	92	12	the	the	DET
ejpam-3153	92	13	moment	moment	NOUN
ejpam-3153	92	14	representation	representation	NOUN
ejpam-3153	92	15	of	of	ADP
ejpam-3153	92	16	daehee	daehee	NOUN
ejpam-3153	92	17	numbers[4	numbers[4	SYM
ejpam-3153	92	18	]	]	X
ejpam-3153	92	19	dn	dn	NOUN
ejpam-3153	92	20	=	=	SYM
ejpam-3153	92	21	(	(	PUNCT
ejpam-3153	92	22	−1)ne(uγ)n	−1)ne(uγ)n	X
ejpam-3153	92	23	.	.	PROPN
ejpam-3153	93	1	(	(	PUNCT
ejpam-3153	93	2	20	20	NUM
ejpam-3153	93	3	)	)	PUNCT
ejpam-3153	93	4	theorem	theorem	NOUN
ejpam-3153	93	5	2	2	NUM
ejpam-3153	93	6	.	.	PUNCT
ejpam-3153	93	7	suppose	suppose	VERB
ejpam-3153	93	8	that	that	SCONJ
ejpam-3153	93	9	r.v	r.v	VERB
ejpam-3153	93	10	u	u	NOUN
ejpam-3153	93	11	∼	∼	NOUN
ejpam-3153	93	12	u	u	NOUN
ejpam-3153	93	13	[	[	X
ejpam-3153	93	14	0	0	NUM
ejpam-3153	93	15	,	,	PUNCT
ejpam-3153	93	16	1	1	NUM
ejpam-3153	93	17	]	]	PUNCT
ejpam-3153	93	18	,	,	PUNCT
ejpam-3153	93	19	γ	γ	X
ejpam-3153	93	20	∼	∼	NOUN
ejpam-3153	93	21	γ(1	γ(1	PROPN
ejpam-3153	93	22	,	,	PUNCT
ejpam-3153	93	23	1	1	NUM
ejpam-3153	93	24	)	)	PUNCT
ejpam-3153	93	25	,	,	PUNCT
ejpam-3153	93	26	r.v	r.v	PROPN
ejpam-3153	93	27	u	u	NOUN
ejpam-3153	93	28	and	and	CCONJ
ejpam-3153	93	29	γ	γ	NOUN
ejpam-3153	93	30	are	be	AUX
ejpam-3153	93	31	independent	independent	ADJ
ejpam-3153	93	32	,	,	PUNCT
ejpam-3153	93	33	then	then	ADV
ejpam-3153	93	34	twisted	twisted	ADJ
ejpam-3153	93	35	daehee	daehee	NOUN
ejpam-3153	93	36	numbers	number	NOUN
ejpam-3153	93	37	of	of	ADP
ejpam-3153	93	38	the	the	DET
ejpam-3153	93	39	second	second	ADJ
ejpam-3153	93	40	kind	kind	NOUN
ejpam-3153	93	41	of	of	ADP
ejpam-3153	93	42	order	order	NOUN
ejpam-3153	93	43	k	k	PROPN
ejpam-3153	93	44	satisfy	satisfy	VERB
ejpam-3153	93	45	d̂	d̂	PROPN
ejpam-3153	93	46	(	(	PUNCT
ejpam-3153	93	47	k	k	NOUN
ejpam-3153	93	48	)	)	PUNCT
ejpam-3153	93	49	n	n	CCONJ
ejpam-3153	93	50	,	,	PUNCT
ejpam-3153	93	51	ξ	ξ	X
ejpam-3153	93	52	=	=	SYM
ejpam-3153	93	53	n∑	n∑	PROPN
ejpam-3153	93	54	i=0	i=0	PROPN
ejpam-3153	93	55	(	(	PUNCT
ejpam-3153	93	56	n	n	NOUN
ejpam-3153	93	57	i	i	NOUN
ejpam-3153	93	58	)	)	PUNCT
ejpam-3153	94	1	ξn−i(k)n−id	ξn−i(k)n−id	PROPN
ejpam-3153	94	2	(	(	PUNCT
ejpam-3153	94	3	k	k	X
ejpam-3153	94	4	)	)	PUNCT
ejpam-3153	94	5	i	i	PROPN
ejpam-3153	94	6	,	,	PUNCT
ejpam-3153	94	7	ξ	ξ	PROPN
ejpam-3153	94	8	.	.	PUNCT
ejpam-3153	95	1	(	(	PUNCT
ejpam-3153	95	2	21	21	NUM
ejpam-3153	95	3	)	)	PUNCT
ejpam-3153	95	4	proof	proof	NOUN
ejpam-3153	95	5	.	.	PUNCT
ejpam-3153	96	1	the	the	DET
ejpam-3153	96	2	generating	generate	VERB
ejpam-3153	96	3	function	function	NOUN
ejpam-3153	96	4	of	of	ADP
ejpam-3153	96	5	d̂	d̂	PROPN
ejpam-3153	96	6	(	(	PUNCT
ejpam-3153	96	7	k	k	NOUN
ejpam-3153	96	8	)	)	PUNCT
ejpam-3153	96	9	n	n	CCONJ
ejpam-3153	96	10	,	,	PUNCT
ejpam-3153	96	11	ξ	ξ	PROPN
ejpam-3153	96	12	is	be	AUX
ejpam-3153	96	13	given	give	VERB
ejpam-3153	96	14	by	by	ADP
ejpam-3153	96	15	(	(	PUNCT
ejpam-3153	96	16	ln(1	ln(1	PROPN
ejpam-3153	96	17	+	+	NUM
ejpam-3153	96	18	ξt	ξt	X
ejpam-3153	96	19	)	)	PUNCT
ejpam-3153	96	20	ξt	ξt	NOUN
ejpam-3153	96	21	(	(	PUNCT
ejpam-3153	96	22	1	1	NUM
ejpam-3153	96	23	+	+	NUM
ejpam-3153	96	24	ξt))k	ξt))k	PROPN
ejpam-3153	96	25	=	=	SYM
ejpam-3153	96	26	∞∑	∞∑	PROPN
ejpam-3153	96	27	n=0	n=0	NUM
ejpam-3153	96	28	d̂	d̂	PROPN
ejpam-3153	96	29	(	(	PUNCT
ejpam-3153	96	30	k	k	NOUN
ejpam-3153	96	31	)	)	PUNCT
ejpam-3153	96	32	n	n	CCONJ
ejpam-3153	96	33	,	,	PUNCT
ejpam-3153	96	34	ξ	ξ	PROPN
ejpam-3153	96	35	tn	tn	PROPN
ejpam-3153	96	36	n	n	X
ejpam-3153	96	37	!	!	PUNCT
ejpam-3153	96	38	.	.	PUNCT
ejpam-3153	97	1	(	(	PUNCT
ejpam-3153	97	2	22	22	NUM
ejpam-3153	97	3	)	)	PUNCT
ejpam-3153	97	4	from	from	ADP
ejpam-3153	97	5	theorem	theorem	ADJ
ejpam-3153	97	6	1	1	NUM
ejpam-3153	97	7	,	,	PUNCT
ejpam-3153	97	8	the	the	DET
ejpam-3153	97	9	left	left	ADJ
ejpam-3153	97	10	-	-	PUNCT
ejpam-3153	97	11	hand	hand	NOUN
ejpam-3153	97	12	side	side	NOUN
ejpam-3153	97	13	of	of	ADP
ejpam-3153	97	14	eq.(22	eq.(22	NOUN
ejpam-3153	97	15	)	)	PUNCT
ejpam-3153	97	16	can	can	AUX
ejpam-3153	97	17	be	be	AUX
ejpam-3153	97	18	written	write	VERB
ejpam-3153	97	19	as	as	ADP
ejpam-3153	97	20	(	(	PUNCT
ejpam-3153	97	21	ln(1	ln(1	PROPN
ejpam-3153	97	22	+	+	NUM
ejpam-3153	97	23	ξt	ξt	X
ejpam-3153	97	24	)	)	PUNCT
ejpam-3153	97	25	ξt	ξt	NOUN
ejpam-3153	97	26	)	)	PUNCT
ejpam-3153	97	27	k(1	k(1	NOUN
ejpam-3153	97	28	+	+	CCONJ
ejpam-3153	97	29	ξt)k	ξt)k	PROPN
ejpam-3153	97	30	=	=	PUNCT
ejpam-3153	98	1	∞∑	∞∑	ADJ
ejpam-3153	98	2	n=0	n=0	NUM
ejpam-3153	98	3	(	(	PUNCT
ejpam-3153	98	4	−ξ)ne(u1γ1	−ξ)ne(u1γ1	NOUN
ejpam-3153	98	5	+	+	CCONJ
ejpam-3153	98	6	u2γ2	u2γ2	PUNCT
ejpam-3153	98	7	+	+	NUM
ejpam-3153	98	8	·	·	PUNCT
ejpam-3153	98	9	·	·	PUNCT
ejpam-3153	98	10	·	·	PUNCT
ejpam-3153	98	11	+	+	NUM
ejpam-3153	98	12	ukγk	ukγk	X
ejpam-3153	98	13	)	)	PUNCT
ejpam-3153	98	14	n	n	ADP
ejpam-3153	98	15	t	t	PROPN
ejpam-3153	98	16	n	n	PRON
ejpam-3153	98	17	n	n	CCONJ
ejpam-3153	98	18	!	!	PUNCT
ejpam-3153	99	1	∞∑	∞∑	NUM
ejpam-3153	99	2	n=0	n=0	NUM
ejpam-3153	99	3	(	(	PUNCT
ejpam-3153	99	4	k)n	k)n	X
ejpam-3153	99	5	(	(	PUNCT
ejpam-3153	99	6	ξt)n	ξt)n	NOUN
ejpam-3153	99	7	n	n	NOUN
ejpam-3153	99	8	!	!	PUNCT
ejpam-3153	99	9	=	=	NOUN
ejpam-3153	100	1	∞∑	∞∑	PRON
ejpam-3153	100	2	n=0	n=0	NUM
ejpam-3153	100	3	n∑	n∑	NOUN
ejpam-3153	100	4	i=0	i=0	PROPN
ejpam-3153	100	5	(	(	PUNCT
ejpam-3153	100	6	n	n	NOUN
ejpam-3153	100	7	i	i	NOUN
ejpam-3153	100	8	)	)	PUNCT
ejpam-3153	100	9	(	(	PUNCT
ejpam-3153	100	10	−ξ)ie(u1γ1	−ξ)ie(u1γ1	NOUN
ejpam-3153	101	1	+	+	CCONJ
ejpam-3153	101	2	u2γ2	u2γ2	X
ejpam-3153	101	3	+	+	NUM
ejpam-3153	101	4	·	·	PUNCT
ejpam-3153	101	5	·	·	PUNCT
ejpam-3153	101	6	·	·	PUNCT
ejpam-3153	101	7	+	+	NUM
ejpam-3153	101	8	ukγk	ukγk	ADJ
ejpam-3153	101	9	)	)	PUNCT
ejpam-3153	101	10	i(k)n−iξ	i(k)n−iξ	PROPN
ejpam-3153	101	11	n−i	n−i	PROPN
ejpam-3153	101	12	t	t	NOUN
ejpam-3153	101	13	n	n	NOUN
ejpam-3153	101	14	n	n	ADV
ejpam-3153	101	15	!	!	PUNCT
ejpam-3153	101	16	=	=	NOUN
ejpam-3153	102	1	∞∑	∞∑	PRON
ejpam-3153	102	2	n=0	n=0	NUM
ejpam-3153	102	3	n∑	n∑	NOUN
ejpam-3153	102	4	i=0	i=0	PROPN
ejpam-3153	102	5	(	(	PUNCT
ejpam-3153	102	6	n	n	NOUN
ejpam-3153	102	7	i	i	NOUN
ejpam-3153	102	8	)	)	PUNCT
ejpam-3153	102	9	ξn−i(k)n−id	ξn−i(k)n−id	PROPN
ejpam-3153	102	10	(	(	PUNCT
ejpam-3153	102	11	k	k	X
ejpam-3153	102	12	)	)	PUNCT
ejpam-3153	102	13	i	i	PRON
ejpam-3153	102	14	,	,	PUNCT
ejpam-3153	102	15	ξ	ξ	PROPN
ejpam-3153	102	16	tn	tn	PROPN
ejpam-3153	102	17	n	n	X
ejpam-3153	102	18	!	!	PROPN
ejpam-3153	102	19	,	,	PUNCT
ejpam-3153	102	20	where	where	SCONJ
ejpam-3153	102	21	(	(	PUNCT
ejpam-3153	102	22	k)n	k)n	X
ejpam-3153	102	23	=	=	SYM
ejpam-3153	102	24	k(k	k(k	NOUN
ejpam-3153	102	25	−	−	NOUN
ejpam-3153	102	26	1	1	NUM
ejpam-3153	102	27	)	)	PUNCT
ejpam-3153	102	28	·	·	PUNCT
ejpam-3153	102	29	·	·	PUNCT
ejpam-3153	102	30	·	·	PUNCT
ejpam-3153	102	31	(	(	PUNCT
ejpam-3153	102	32	k	k	X
ejpam-3153	102	33	−	−	PROPN
ejpam-3153	102	34	n+	n+	NOUN
ejpam-3153	102	35	1	1	NUM
ejpam-3153	102	36	)	)	PUNCT
ejpam-3153	102	37	.	.	PUNCT
ejpam-3153	103	1	by	by	ADP
ejpam-3153	103	2	comparing	compare	VERB
ejpam-3153	103	3	the	the	DET
ejpam-3153	103	4	coefficients	coefficient	NOUN
ejpam-3153	103	5	of	of	ADP
ejpam-3153	103	6	tn	tn	NOUN
ejpam-3153	103	7	n	n	CCONJ
ejpam-3153	103	8	!	!	PROPN
ejpam-3153	103	9	,	,	PUNCT
ejpam-3153	103	10	theorem	theorem	VERB
ejpam-3153	103	11	2	2	NUM
ejpam-3153	103	12	is	be	AUX
ejpam-3153	103	13	proved	prove	VERB
ejpam-3153	103	14	.	.	PUNCT
ejpam-3153	104	1	c.	c.	PROPN
ejpam-3153	104	2	liu	liu	PROPN
ejpam-3153	104	3	,	,	PUNCT
ejpam-3153	104	4	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	104	5	/	/	SYM
ejpam-3153	104	6	eur	eur	PROPN
ejpam-3153	104	7	.	.	PUNCT
ejpam-3153	105	1	j.	j.	PROPN
ejpam-3153	105	2	pure	pure	PROPN
ejpam-3153	105	3	appl	appl	PROPN
ejpam-3153	105	4	.	.	PROPN
ejpam-3153	105	5	math	math	PROPN
ejpam-3153	105	6	,	,	PUNCT
ejpam-3153	105	7	11	11	NUM
ejpam-3153	105	8	(	(	PUNCT
ejpam-3153	105	9	1	1	NUM
ejpam-3153	105	10	)	)	PUNCT
ejpam-3153	105	11	(	(	PUNCT
ejpam-3153	105	12	2018	2018	NUM
ejpam-3153	105	13	)	)	PUNCT
ejpam-3153	105	14	,	,	PUNCT
ejpam-3153	105	15	69	69	NUM
ejpam-3153	105	16	-	-	SYM
ejpam-3153	105	17	78	78	NUM
ejpam-3153	105	18	74	74	NUM
ejpam-3153	105	19	corollary	corollary	ADJ
ejpam-3153	105	20	4	4	NUM
ejpam-3153	105	21	.	.	PUNCT
ejpam-3153	105	22	in	in	ADP
ejpam-3153	105	23	theorem	theorem	NOUN
ejpam-3153	105	24	2	2	NUM
ejpam-3153	105	25	,	,	PUNCT
ejpam-3153	105	26	taking	take	VERB
ejpam-3153	105	27	k	k	X
ejpam-3153	105	28	=	=	SYM
ejpam-3153	105	29	1	1	NUM
ejpam-3153	105	30	,	,	PUNCT
ejpam-3153	105	31	n	n	CCONJ
ejpam-3153	105	32	>	>	X
ejpam-3153	105	33	1	1	NUM
ejpam-3153	105	34	,	,	PUNCT
ejpam-3153	105	35	we	we	PRON
ejpam-3153	105	36	obtain	obtain	VERB
ejpam-3153	105	37	the	the	DET
ejpam-3153	105	38	moment	moment	NOUN
ejpam-3153	105	39	form	form	NOUN
ejpam-3153	105	40	of	of	ADP
ejpam-3153	105	41	twisted	twisted	ADJ
ejpam-3153	105	42	daehee	daehee	NOUN
ejpam-3153	105	43	numbers	number	NOUN
ejpam-3153	105	44	of	of	ADP
ejpam-3153	105	45	the	the	DET
ejpam-3153	105	46	second	second	ADJ
ejpam-3153	105	47	kind	kind	NOUN
ejpam-3153	105	48	,	,	PUNCT
ejpam-3153	105	49	d̂n	d̂n	NOUN
ejpam-3153	105	50	,	,	PUNCT
ejpam-3153	105	51	ξ	ξ	X
ejpam-3153	105	52	=	=	SYM
ejpam-3153	105	53	(	(	PUNCT
ejpam-3153	105	54	−1)n−1	−1)n−1	PROPN
ejpam-3153	105	55	n	n	PROPN
ejpam-3153	105	56	ξne(uγ)n	ξne(uγ)n	PROPN
ejpam-3153	105	57	,	,	PUNCT
ejpam-3153	105	58	n	n	PROPN
ejpam-3153	105	59	>	>	X
ejpam-3153	105	60	1	1	NUM
ejpam-3153	105	61	,	,	PUNCT
ejpam-3153	105	62	d̂0,ξ	d̂0,ξ	VERB
ejpam-3153	105	63	=	=	NOUN
ejpam-3153	105	64	1	1	X
ejpam-3153	105	65	.	.	PUNCT
ejpam-3153	105	66	(	(	PUNCT
ejpam-3153	105	67	23	23	NUM
ejpam-3153	105	68	)	)	PUNCT
ejpam-3153	105	69	corollary	corollary	ADJ
ejpam-3153	105	70	5	5	NUM
ejpam-3153	105	71	.	.	PUNCT
ejpam-3153	105	72	from	from	ADP
ejpam-3153	105	73	corollary	corollary	ADJ
ejpam-3153	105	74	2	2	NUM
ejpam-3153	105	75	and	and	CCONJ
ejpam-3153	105	76	corollary	corollary	ADJ
ejpam-3153	105	77	4	4	NUM
ejpam-3153	105	78	,	,	PUNCT
ejpam-3153	105	79	when	when	SCONJ
ejpam-3153	105	80	n	n	X
ejpam-3153	105	81	>	>	X
ejpam-3153	105	82	1,the	1,the	NUM
ejpam-3153	105	83	following	follow	VERB
ejpam-3153	105	84	relationship	relationship	NOUN
ejpam-3153	105	85	holds	hold	VERB
ejpam-3153	105	86	true	true	ADJ
ejpam-3153	105	87	,	,	PUNCT
ejpam-3153	105	88	−nd̂n	−nd̂n	PROPN
ejpam-3153	105	89	,	,	PUNCT
ejpam-3153	105	90	ξ	ξ	X
ejpam-3153	105	91	=	=	SYM
ejpam-3153	105	92	dn	dn	PROPN
ejpam-3153	105	93	,	,	PUNCT
ejpam-3153	105	94	ξ	ξ	PROPN
ejpam-3153	105	95	,	,	PUNCT
ejpam-3153	105	96	n	n	PROPN
ejpam-3153	105	97	>	>	X
ejpam-3153	105	98	1	1	NUM
ejpam-3153	105	99	.	.	PUNCT
ejpam-3153	106	1	(	(	PUNCT
ejpam-3153	106	2	24	24	NUM
ejpam-3153	106	3	)	)	PUNCT
ejpam-3153	106	4	theorem	theorem	NOUN
ejpam-3153	106	5	3	3	NUM
ejpam-3153	106	6	.	.	PUNCT
ejpam-3153	107	1	under	under	ADP
ejpam-3153	107	2	the	the	DET
ejpam-3153	107	3	circumstance	circumstance	NOUN
ejpam-3153	107	4	of	of	ADP
ejpam-3153	107	5	theorem	theorem	ADJ
ejpam-3153	107	6	1	1	NUM
ejpam-3153	107	7	,	,	PUNCT
ejpam-3153	107	8	higher	high	ADJ
ejpam-3153	107	9	-	-	PUNCT
ejpam-3153	107	10	order	order	NOUN
ejpam-3153	107	11	twisted	twisted	ADJ
ejpam-3153	107	12	daehee	daehee	NOUN
ejpam-3153	107	13	polynomials	polynomial	NOUN
ejpam-3153	107	14	d	d	X
ejpam-3153	107	15	(	(	PUNCT
ejpam-3153	107	16	k	k	NOUN
ejpam-3153	107	17	)	)	PUNCT
ejpam-3153	107	18	n	n	CCONJ
ejpam-3153	107	19	,	,	PUNCT
ejpam-3153	107	20	ξ(x	ξ(x	NOUN
ejpam-3153	107	21	)	)	PUNCT
ejpam-3153	107	22	have	have	VERB
ejpam-3153	107	23	the	the	DET
ejpam-3153	107	24	following	following	ADJ
ejpam-3153	107	25	moment	moment	NOUN
ejpam-3153	107	26	representation3	representation3	PROPN
ejpam-3153	108	1	d	d	X
ejpam-3153	108	2	(	(	PUNCT
ejpam-3153	108	3	k	k	NOUN
ejpam-3153	108	4	)	)	PUNCT
ejpam-3153	108	5	n	n	CCONJ
ejpam-3153	108	6	,	,	PUNCT
ejpam-3153	108	7	ξ(x	ξ(x	NOUN
ejpam-3153	108	8	)	)	PUNCT
ejpam-3153	108	9	=	=	SYM
ejpam-3153	109	1	n∑	n∑	PROPN
ejpam-3153	109	2	i=0	i=0	PROPN
ejpam-3153	109	3	(	(	PUNCT
ejpam-3153	109	4	n	n	X
ejpam-3153	109	5	i	i	NOUN
ejpam-3153	109	6	)	)	PUNCT
ejpam-3153	109	7	ξn−i(x)n−id	ξn−i(x)n−id	PROPN
ejpam-3153	109	8	(	(	PUNCT
ejpam-3153	109	9	k	k	X
ejpam-3153	109	10	)	)	PUNCT
ejpam-3153	109	11	i	i	PROPN
ejpam-3153	109	12	,	,	PUNCT
ejpam-3153	109	13	ξ	ξ	PROPN
ejpam-3153	109	14	.	.	PUNCT
ejpam-3153	110	1	(	(	PUNCT
ejpam-3153	110	2	25	25	NUM
ejpam-3153	110	3	)	)	PUNCT
ejpam-3153	110	4	proof	proof	NOUN
ejpam-3153	110	5	.	.	PUNCT
ejpam-3153	111	1	proof	proof	NOUN
ejpam-3153	111	2	of	of	ADP
ejpam-3153	111	3	theorem	theorem	ADJ
ejpam-3153	111	4	3	3	NUM
ejpam-3153	111	5	is	be	AUX
ejpam-3153	111	6	similar	similar	ADJ
ejpam-3153	111	7	to	to	ADP
ejpam-3153	111	8	the	the	DET
ejpam-3153	111	9	one	one	NUM
ejpam-3153	111	10	of	of	ADP
ejpam-3153	111	11	theorem	theorem	ADJ
ejpam-3153	111	12	2	2	NUM
ejpam-3153	111	13	.	.	PUNCT
ejpam-3153	111	14	theorem	theorem	NOUN
ejpam-3153	111	15	4	4	NUM
ejpam-3153	111	16	.	.	PUNCT
ejpam-3153	111	17	suppose	suppose	VERB
ejpam-3153	111	18	that	that	SCONJ
ejpam-3153	111	19	r.v.s	r.v.s	NOUN
ejpam-3153	111	20	u1	u1	NOUN
ejpam-3153	111	21	,	,	PUNCT
ejpam-3153	111	22	u2	u2	NOUN
ejpam-3153	111	23	,	,	PUNCT
ejpam-3153	111	24	...	...	PUNCT
ejpam-3153	111	25	,	,	PUNCT
ejpam-3153	111	26	i.i.d	i.i.d	ADP
ejpam-3153	111	27	∼	∼	NOUN
ejpam-3153	111	28	u	u	NOUN
ejpam-3153	111	29	[	[	X
ejpam-3153	111	30	0	0	NUM
ejpam-3153	111	31	,	,	PUNCT
ejpam-3153	111	32	1	1	NUM
ejpam-3153	111	33	]	]	PUNCT
ejpam-3153	111	34	,	,	PUNCT
ejpam-3153	111	35	γ1,γ2	γ1,γ2	PROPN
ejpam-3153	111	36	,	,	PUNCT
ejpam-3153	111	37	...	...	PUNCT
ejpam-3153	111	38	,	,	PUNCT
ejpam-3153	111	39	i.i.d	i.i.d	ADP
ejpam-3153	111	40	∼	∼	NOUN
ejpam-3153	111	41	γ(1	γ(1	PROPN
ejpam-3153	111	42	,	,	PUNCT
ejpam-3153	111	43	1	1	NUM
ejpam-3153	111	44	)	)	PUNCT
ejpam-3153	111	45	,	,	PUNCT
ejpam-3153	111	46	x	x	X
ejpam-3153	111	47	∼	∼	NOUN
ejpam-3153	111	48	γ[−x	γ[−x	NOUN
ejpam-3153	111	49	,	,	PUNCT
ejpam-3153	111	50	1	1	NUM
ejpam-3153	111	51	ξ	ξ	X
ejpam-3153	111	52	]	]	PUNCT
ejpam-3153	111	53	,	,	PUNCT
ejpam-3153	111	54	(	(	PUNCT
ejpam-3153	111	55	x	x	SYM
ejpam-3153	111	56	<	<	X
ejpam-3153	111	57	0	0	NUM
ejpam-3153	111	58	,	,	PUNCT
ejpam-3153	111	59	ξ	ξ	X
ejpam-3153	111	60	>	>	X
ejpam-3153	111	61	0	0	NUM
ejpam-3153	111	62	)	)	PUNCT
ejpam-3153	111	63	,	,	PUNCT
ejpam-3153	111	64	and	and	CCONJ
ejpam-3153	111	65	r.v	r.v	PROPN
ejpam-3153	111	66	ui	ui	PROPN
ejpam-3153	111	67	,	,	PUNCT
ejpam-3153	111	68	γj	γj	ADP
ejpam-3153	111	69	and	and	CCONJ
ejpam-3153	111	70	x	x	PRON
ejpam-3153	111	71	are	be	AUX
ejpam-3153	111	72	independent	independent	ADJ
ejpam-3153	111	73	for	for	ADP
ejpam-3153	111	74	all	all	DET
ejpam-3153	111	75	i	i	PROPN
ejpam-3153	111	76	,	,	PUNCT
ejpam-3153	111	77	j	j	PROPN
ejpam-3153	111	78	,	,	PUNCT
ejpam-3153	111	79	then	then	ADV
ejpam-3153	111	80	higher	high	ADJ
ejpam-3153	111	81	-	-	PUNCT
ejpam-3153	111	82	order	order	NOUN
ejpam-3153	111	83	twisted	twisted	ADJ
ejpam-3153	111	84	daehee	daehee	NOUN
ejpam-3153	111	85	polynomials	polynomial	NOUN
ejpam-3153	112	1	d	d	X
ejpam-3153	112	2	(	(	PUNCT
ejpam-3153	112	3	k	k	NOUN
ejpam-3153	112	4	)	)	PUNCT
ejpam-3153	112	5	n	n	CCONJ
ejpam-3153	112	6	,	,	PUNCT
ejpam-3153	112	7	ξ(x	ξ(x	NOUN
ejpam-3153	112	8	)	)	PUNCT
ejpam-3153	112	9	satisfy	satisfy	NOUN
ejpam-3153	112	10	d	d	X
ejpam-3153	112	11	(	(	PUNCT
ejpam-3153	112	12	k	k	NOUN
ejpam-3153	112	13	)	)	PUNCT
ejpam-3153	112	14	n	n	CCONJ
ejpam-3153	112	15	,	,	PUNCT
ejpam-3153	112	16	ξ(x	ξ(x	NOUN
ejpam-3153	112	17	)	)	PUNCT
ejpam-3153	112	18	=	=	SYM
ejpam-3153	112	19	e[ξ(u1γ1	e[ξ(u1γ1	NOUN
ejpam-3153	112	20	+	+	NOUN
ejpam-3153	112	21	·	·	PUNCT
ejpam-3153	112	22	·	·	PUNCT
ejpam-3153	112	23	·	·	PUNCT
ejpam-3153	112	24	+	+	NUM
ejpam-3153	112	25	ukγk	ukγk	NOUN
ejpam-3153	112	26	)	)	PUNCT
ejpam-3153	112	27	+	+	NOUN
ejpam-3153	112	28	x]n	x]n	PROPN
ejpam-3153	112	29	.	.	PUNCT
ejpam-3153	113	1	(	(	PUNCT
ejpam-3153	113	2	26	26	NUM
ejpam-3153	113	3	)	)	PUNCT
ejpam-3153	113	4	proof	proof	NOUN
ejpam-3153	113	5	.	.	PUNCT
ejpam-3153	114	1	replacing	replace	VERB
ejpam-3153	114	2	t	t	NOUN
ejpam-3153	114	3	by	by	ADP
ejpam-3153	114	4	−it	−it	PROPN
ejpam-3153	114	5	in	in	ADP
ejpam-3153	114	6	the	the	DET
ejpam-3153	114	7	generating	generate	VERB
ejpam-3153	114	8	function	function	NOUN
ejpam-3153	114	9	of	of	ADP
ejpam-3153	114	10	higher	high	ADJ
ejpam-3153	114	11	-	-	PUNCT
ejpam-3153	114	12	order	order	NOUN
ejpam-3153	114	13	twisted	twisted	ADJ
ejpam-3153	114	14	daehee	daehee	NOUN
ejpam-3153	114	15	polynomials	polynomial	NOUN
ejpam-3153	114	16	,	,	PUNCT
ejpam-3153	114	17	and	and	CCONJ
ejpam-3153	114	18	according	accord	VERB
ejpam-3153	114	19	to	to	PART
ejpam-3153	114	20	remark	remark	NOUN
ejpam-3153	114	21	3	3	NUM
ejpam-3153	114	22	and	and	CCONJ
ejpam-3153	114	23	4	4	NUM
ejpam-3153	114	24	,	,	PUNCT
ejpam-3153	114	25	we	we	PRON
ejpam-3153	114	26	have	have	VERB
ejpam-3153	114	27	∞∑	∞∑	NUM
ejpam-3153	114	28	n=0	n=0	NUM
ejpam-3153	114	29	d	d	NOUN
ejpam-3153	114	30	(	(	PUNCT
ejpam-3153	114	31	k	k	NOUN
ejpam-3153	114	32	)	)	PUNCT
ejpam-3153	114	33	n	n	CCONJ
ejpam-3153	114	34	,	,	PUNCT
ejpam-3153	114	35	ξ(x	ξ(x	NOUN
ejpam-3153	114	36	)	)	PUNCT
ejpam-3153	114	37	(	(	PUNCT
ejpam-3153	114	38	−it)n	−it)n	NOUN
ejpam-3153	114	39	n	n	CCONJ
ejpam-3153	114	40	!	!	PUNCT
ejpam-3153	115	1	=	=	PUNCT
ejpam-3153	115	2	(	(	PUNCT
ejpam-3153	115	3	ln(1−	ln(1−	ADJ
ejpam-3153	115	4	ξit	ξit	NOUN
ejpam-3153	115	5	)	)	PUNCT
ejpam-3153	115	6	−ξit	−ξit	NOUN
ejpam-3153	115	7	)	)	PUNCT
ejpam-3153	115	8	k(1−	k(1−	PROPN
ejpam-3153	115	9	ξit)−(−x	ξit)−(−x	NOUN
ejpam-3153	115	10	)	)	PUNCT
ejpam-3153	116	1	=	=	PUNCT
ejpam-3153	117	1	∞∑	∞∑	NUM
ejpam-3153	117	2	n=0	n=0	PUNCT
ejpam-3153	117	3	(	(	PUNCT
ejpam-3153	117	4	−1)nξne(u1γ1	−1)nξne(u1γ1	CCONJ
ejpam-3153	117	5	+	+	X
ejpam-3153	117	6	·	·	PUNCT
ejpam-3153	117	7	·	·	PUNCT
ejpam-3153	117	8	·	·	PUNCT
ejpam-3153	117	9	+	+	NUM
ejpam-3153	117	10	ukγk	ukγk	X
ejpam-3153	117	11	)	)	PUNCT
ejpam-3153	117	12	n	n	CCONJ
ejpam-3153	117	13	(	(	PUNCT
ejpam-3153	117	14	−it)n	−it)n	NOUN
ejpam-3153	117	15	n	n	CCONJ
ejpam-3153	117	16	!	!	PUNCT
ejpam-3153	118	1	∞∑	∞∑	ADJ
ejpam-3153	118	2	n=0	n=0	PUNCT
ejpam-3153	118	3	exn	exn	NOUN
ejpam-3153	118	4	(	(	PUNCT
ejpam-3153	118	5	it)n	it)n	PROPN
ejpam-3153	118	6	n	n	NUM
ejpam-3153	118	7	!	!	PUNCT
ejpam-3153	118	8	=	=	NOUN
ejpam-3153	119	1	∞∑	∞∑	PRON
ejpam-3153	119	2	n=0	n=0	NUM
ejpam-3153	119	3	n∑	n∑	NOUN
ejpam-3153	119	4	i=0	i=0	PROPN
ejpam-3153	119	5	(	(	PUNCT
ejpam-3153	119	6	n	n	NOUN
ejpam-3153	119	7	i	i	PROPN
ejpam-3153	119	8	)	)	PUNCT
ejpam-3153	119	9	ξie(u1γ1	ξie(u1γ1	PROPN
ejpam-3153	119	10	+	+	CCONJ
ejpam-3153	119	11	·	·	PUNCT
ejpam-3153	119	12	·	·	PUNCT
ejpam-3153	119	13	·	·	PUNCT
ejpam-3153	119	14	+	+	NUM
ejpam-3153	119	15	ukγk	ukγk	NOUN
ejpam-3153	119	16	)	)	PUNCT
ejpam-3153	119	17	iexn−i	iexn−i	VERB
ejpam-3153	119	18	(	(	PUNCT
ejpam-3153	119	19	it	it	PRON
ejpam-3153	119	20	)	)	PUNCT
ejpam-3153	119	21	n	n	PRON
ejpam-3153	119	22	n	n	CCONJ
ejpam-3153	119	23	!	!	PUNCT
ejpam-3153	120	1	=	=	PUNCT
ejpam-3153	121	1	∞∑	∞∑	PRON
ejpam-3153	121	2	n=0	n=0	NUM
ejpam-3153	121	3	e[ξ(u1γ1	e[ξ(u1γ1	NOUN
ejpam-3153	121	4	+	+	X
ejpam-3153	121	5	·	·	PUNCT
ejpam-3153	121	6	·	·	PUNCT
ejpam-3153	121	7	·	·	PUNCT
ejpam-3153	121	8	+	+	NUM
ejpam-3153	121	9	ukγk	ukγk	NOUN
ejpam-3153	121	10	)	)	PUNCT
ejpam-3153	122	1	+	+	ADJ
ejpam-3153	122	2	x]n	x]n	PROPN
ejpam-3153	122	3	itn	itn	PROPN
ejpam-3153	122	4	n	n	PRON
ejpam-3153	122	5	!	!	PUNCT
ejpam-3153	122	6	.	.	PUNCT
ejpam-3153	123	1	by	by	ADP
ejpam-3153	123	2	comparing	compare	VERB
ejpam-3153	123	3	the	the	DET
ejpam-3153	123	4	coefficients	coefficient	NOUN
ejpam-3153	123	5	of	of	ADP
ejpam-3153	123	6	(	(	PUNCT
ejpam-3153	123	7	it)n	it)n	PROPN
ejpam-3153	123	8	n	n	X
ejpam-3153	123	9	!	!	PUNCT
ejpam-3153	123	10	,	,	PUNCT
ejpam-3153	123	11	we	we	PRON
ejpam-3153	123	12	obtain	obtain	AUX
ejpam-3153	123	13	theorem	theorem	ADJ
ejpam-3153	123	14	4	4	NUM
ejpam-3153	123	15	.	.	PUNCT
ejpam-3153	123	16	theorem	theorem	NOUN
ejpam-3153	123	17	5	5	NUM
ejpam-3153	123	18	.	.	PUNCT
ejpam-3153	123	19	suppose	suppose	VERB
ejpam-3153	123	20	that	that	SCONJ
ejpam-3153	123	21	r.v	r.v	VERB
ejpam-3153	123	22	u	u	NOUN
ejpam-3153	123	23	∼	∼	NOUN
ejpam-3153	123	24	u	u	NOUN
ejpam-3153	123	25	[	[	X
ejpam-3153	123	26	0	0	NUM
ejpam-3153	123	27	,	,	PUNCT
ejpam-3153	123	28	1	1	NUM
ejpam-3153	123	29	]	]	PUNCT
ejpam-3153	123	30	,	,	PUNCT
ejpam-3153	123	31	γ	γ	X
ejpam-3153	123	32	∼	∼	NOUN
ejpam-3153	123	33	γ(1	γ(1	PROPN
ejpam-3153	123	34	,	,	PUNCT
ejpam-3153	123	35	1	1	NUM
ejpam-3153	123	36	)	)	PUNCT
ejpam-3153	123	37	,	,	PUNCT
ejpam-3153	123	38	r.v	r.v	PROPN
ejpam-3153	123	39	u	u	NOUN
ejpam-3153	123	40	and	and	CCONJ
ejpam-3153	123	41	γ	γ	NOUN
ejpam-3153	123	42	are	be	AUX
ejpam-3153	123	43	independent	independent	ADJ
ejpam-3153	123	44	respectively	respectively	ADV
ejpam-3153	123	45	,	,	PUNCT
ejpam-3153	123	46	twisted	twisted	ADJ
ejpam-3153	123	47	daehee	daehee	NOUN
ejpam-3153	123	48	polynomials	polynomial	NOUN
ejpam-3153	123	49	of	of	ADP
ejpam-3153	123	50	the	the	DET
ejpam-3153	123	51	second	second	ADJ
ejpam-3153	123	52	kind	kind	NOUN
ejpam-3153	123	53	of	of	ADP
ejpam-3153	123	54	order	order	NOUN
ejpam-3153	123	55	k	k	PROPN
ejpam-3153	123	56	satisfy	satisfy	VERB
ejpam-3153	123	57	d̂	d̂	PROPN
ejpam-3153	123	58	(	(	PUNCT
ejpam-3153	123	59	k	k	NOUN
ejpam-3153	123	60	)	)	PUNCT
ejpam-3153	123	61	n	n	CCONJ
ejpam-3153	123	62	,	,	PUNCT
ejpam-3153	123	63	ξ(x	ξ(x	NOUN
ejpam-3153	123	64	)	)	PUNCT
ejpam-3153	124	1	=	=	SYM
ejpam-3153	124	2	n∑	n∑	PROPN
ejpam-3153	124	3	i=0	i=0	PROPN
ejpam-3153	124	4	(	(	PUNCT
ejpam-3153	124	5	n	n	X
ejpam-3153	124	6	i	i	PRON
ejpam-3153	124	7	)	)	PUNCT
ejpam-3153	124	8	ξn(−1)ie(u1γ1	ξn(−1)ie(u1γ1	PROPN
ejpam-3153	124	9	+	+	X
ejpam-3153	124	10	·	·	PUNCT
ejpam-3153	124	11	·	·	PUNCT
ejpam-3153	125	1	·	·	PUNCT
ejpam-3153	125	2	+	+	NUM
ejpam-3153	125	3	ukγk	ukγk	NOUN
ejpam-3153	125	4	)	)	PUNCT
ejpam-3153	126	1	i(x+	i(x+	ADV
ejpam-3153	126	2	k)n−i	k)n−i	X
ejpam-3153	126	3	.	.	PUNCT
ejpam-3153	127	1	(	(	PUNCT
ejpam-3153	127	2	27	27	NUM
ejpam-3153	127	3	)	)	PUNCT
ejpam-3153	127	4	c.	c.	PROPN
ejpam-3153	127	5	liu	liu	PROPN
ejpam-3153	127	6	,	,	PUNCT
ejpam-3153	127	7	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	127	8	/	/	SYM
ejpam-3153	127	9	eur	eur	PROPN
ejpam-3153	127	10	.	.	PUNCT
ejpam-3153	128	1	j.	j.	PROPN
ejpam-3153	128	2	pure	pure	PROPN
ejpam-3153	128	3	appl	appl	PROPN
ejpam-3153	128	4	.	.	PROPN
ejpam-3153	128	5	math	math	PROPN
ejpam-3153	128	6	,	,	PUNCT
ejpam-3153	128	7	11	11	NUM
ejpam-3153	128	8	(	(	PUNCT
ejpam-3153	128	9	1	1	NUM
ejpam-3153	128	10	)	)	PUNCT
ejpam-3153	128	11	(	(	PUNCT
ejpam-3153	128	12	2018	2018	NUM
ejpam-3153	128	13	)	)	PUNCT
ejpam-3153	128	14	,	,	PUNCT
ejpam-3153	128	15	69	69	NUM
ejpam-3153	128	16	-	-	SYM
ejpam-3153	128	17	78	78	NUM
ejpam-3153	128	18	75	75	NUM
ejpam-3153	128	19	proof	proof	NOUN
ejpam-3153	128	20	.	.	PUNCT
ejpam-3153	129	1	proof	proof	NOUN
ejpam-3153	129	2	of	of	ADP
ejpam-3153	129	3	theorem	theorem	ADJ
ejpam-3153	129	4	5	5	NUM
ejpam-3153	129	5	is	be	AUX
ejpam-3153	129	6	similar	similar	ADJ
ejpam-3153	129	7	to	to	ADP
ejpam-3153	129	8	that	that	PRON
ejpam-3153	129	9	of	of	ADP
ejpam-3153	129	10	theorem	theorem	ADJ
ejpam-3153	129	11	2	2	NUM
ejpam-3153	129	12	.	.	PUNCT
ejpam-3153	129	13	theorem	theorem	NOUN
ejpam-3153	129	14	6	6	NUM
ejpam-3153	129	15	.	.	PUNCT
ejpam-3153	129	16	suppose	suppose	VERB
ejpam-3153	129	17	that	that	SCONJ
ejpam-3153	129	18	r.v.s	r.v.s	NOUN
ejpam-3153	129	19	u1	u1	NOUN
ejpam-3153	129	20	,	,	PUNCT
ejpam-3153	129	21	u2	u2	NOUN
ejpam-3153	129	22	,	,	PUNCT
ejpam-3153	129	23	...	...	PUNCT
ejpam-3153	129	24	,	,	PUNCT
ejpam-3153	129	25	i.i.d	i.i.d	ADP
ejpam-3153	129	26	∼	∼	NOUN
ejpam-3153	129	27	u	u	NOUN
ejpam-3153	129	28	[	[	X
ejpam-3153	129	29	0	0	NUM
ejpam-3153	129	30	,	,	PUNCT
ejpam-3153	129	31	1	1	NUM
ejpam-3153	129	32	]	]	PUNCT
ejpam-3153	129	33	,	,	PUNCT
ejpam-3153	129	34	γ1,γ2	γ1,γ2	PROPN
ejpam-3153	129	35	,	,	PUNCT
ejpam-3153	129	36	...	...	PUNCT
ejpam-3153	129	37	,	,	PUNCT
ejpam-3153	129	38	i.i.d	i.i.d	ADP
ejpam-3153	129	39	∼	∼	NOUN
ejpam-3153	129	40	γ(1	γ(1	PROPN
ejpam-3153	129	41	,	,	PUNCT
ejpam-3153	129	42	1	1	NUM
ejpam-3153	129	43	)	)	PUNCT
ejpam-3153	129	44	,	,	PUNCT
ejpam-3153	129	45	x	x	X
ejpam-3153	129	46	∼	∼	NOUN
ejpam-3153	129	47	γ[−x	γ[−x	X
ejpam-3153	129	48	−	−	NOUN
ejpam-3153	130	1	k	k	NOUN
ejpam-3153	130	2	,	,	PUNCT
ejpam-3153	130	3	1	1	NUM
ejpam-3153	130	4	ξ	ξ	NOUN
ejpam-3153	130	5	]	]	PUNCT
ejpam-3153	130	6	,	,	PUNCT
ejpam-3153	130	7	(	(	PUNCT
ejpam-3153	130	8	x	x	X
ejpam-3153	130	9	<	<	X
ejpam-3153	130	10	−k	−k	PROPN
ejpam-3153	130	11	,	,	PUNCT
ejpam-3153	130	12	ξ	ξ	X
ejpam-3153	130	13	>	>	X
ejpam-3153	130	14	0	0	NUM
ejpam-3153	130	15	)	)	PUNCT
ejpam-3153	130	16	,	,	PUNCT
ejpam-3153	130	17	and	and	CCONJ
ejpam-3153	130	18	r.v	r.v	PROPN
ejpam-3153	130	19	ui	ui	PROPN
ejpam-3153	130	20	,	,	PUNCT
ejpam-3153	130	21	γj	γj	ADP
ejpam-3153	130	22	and	and	CCONJ
ejpam-3153	130	23	x	x	PRON
ejpam-3153	130	24	are	be	AUX
ejpam-3153	130	25	independent	independent	ADJ
ejpam-3153	130	26	for	for	ADP
ejpam-3153	130	27	all	all	DET
ejpam-3153	130	28	i	i	PROPN
ejpam-3153	130	29	,	,	PUNCT
ejpam-3153	130	30	j	j	PROPN
ejpam-3153	130	31	,	,	PUNCT
ejpam-3153	130	32	then	then	ADV
ejpam-3153	130	33	higher	high	ADJ
ejpam-3153	130	34	-	-	PUNCT
ejpam-3153	130	35	order	order	NOUN
ejpam-3153	130	36	twisted	twisted	ADJ
ejpam-3153	130	37	daehee	daehee	NOUN
ejpam-3153	130	38	polynomials	polynomial	NOUN
ejpam-3153	130	39	of	of	ADP
ejpam-3153	130	40	the	the	DET
ejpam-3153	130	41	second	second	ADJ
ejpam-3153	130	42	kind	kind	NOUN
ejpam-3153	130	43	d̂	d̂	PROPN
ejpam-3153	130	44	(	(	PUNCT
ejpam-3153	130	45	k	k	NOUN
ejpam-3153	130	46	)	)	PUNCT
ejpam-3153	130	47	n	n	CCONJ
ejpam-3153	130	48	,	,	PUNCT
ejpam-3153	130	49	ξ(x	ξ(x	NOUN
ejpam-3153	130	50	)	)	PUNCT
ejpam-3153	130	51	satisfy	satisfy	NOUN
ejpam-3153	130	52	d̂	d̂	PROPN
ejpam-3153	130	53	(	(	PUNCT
ejpam-3153	130	54	k	k	NOUN
ejpam-3153	130	55	)	)	PUNCT
ejpam-3153	130	56	n	n	CCONJ
ejpam-3153	130	57	,	,	PUNCT
ejpam-3153	130	58	ξ(x	ξ(x	NOUN
ejpam-3153	130	59	)	)	PUNCT
ejpam-3153	130	60	=	=	PUNCT
ejpam-3153	131	1	(	(	PUNCT
ejpam-3153	131	2	−1)ne[ξ(u1γ1	−1)ne[ξ(u1γ1	NOUN
ejpam-3153	131	3	+	+	CCONJ
ejpam-3153	131	4	·	·	PUNCT
ejpam-3153	131	5	·	·	PUNCT
ejpam-3153	131	6	·	·	PUNCT
ejpam-3153	131	7	+	+	NUM
ejpam-3153	131	8	ukγk	ukγk	NOUN
ejpam-3153	131	9	)	)	PUNCT
ejpam-3153	131	10	+	+	NOUN
ejpam-3153	131	11	x]n	x]n	PROPN
ejpam-3153	131	12	.	.	PUNCT
ejpam-3153	132	1	(	(	PUNCT
ejpam-3153	132	2	28	28	NUM
ejpam-3153	132	3	)	)	PUNCT
ejpam-3153	132	4	proof	proof	NOUN
ejpam-3153	132	5	.	.	PUNCT
ejpam-3153	133	1	proof	proof	NOUN
ejpam-3153	133	2	of	of	ADP
ejpam-3153	133	3	theorem	theorem	NOUN
ejpam-3153	133	4	6	6	NUM
ejpam-3153	133	5	is	be	AUX
ejpam-3153	133	6	similar	similar	ADJ
ejpam-3153	133	7	to	to	ADP
ejpam-3153	133	8	the	the	DET
ejpam-3153	133	9	one	one	NUM
ejpam-3153	133	10	of	of	ADP
ejpam-3153	133	11	theorem	theorem	ADJ
ejpam-3153	133	12	4	4	NUM
ejpam-3153	133	13	.	.	PUNCT
ejpam-3153	133	14	theorem	theorem	NOUN
ejpam-3153	133	15	7	7	PROPN
ejpam-3153	133	16	.	.	X
ejpam-3153	133	17	assume	assume	VERB
ejpam-3153	133	18	r.v	r.v	X
ejpam-3153	133	19	x	x	PUNCT
ejpam-3153	133	20	∼	∼	NOUN
ejpam-3153	133	21	γ[r	γ[r	PROPN
ejpam-3153	133	22	,	,	PUNCT
ejpam-3153	133	23	2	2	NUM
ejpam-3153	133	24	]	]	PUNCT
ejpam-3153	133	25	,	,	PUNCT
ejpam-3153	133	26	then	then	ADV
ejpam-3153	133	27	higher	high	ADJ
ejpam-3153	133	28	-	-	PUNCT
ejpam-3153	133	29	order	order	NOUN
ejpam-3153	133	30	changhee	changhee	NOUN
ejpam-3153	133	31	numbers	number	NOUN
ejpam-3153	133	32	satisfy	satisfy	VERB
ejpam-3153	133	33	ch(r	ch(r	NOUN
ejpam-3153	133	34	)	)	PUNCT
ejpam-3153	134	1	n	n	NOUN
ejpam-3153	134	2	=	=	SYM
ejpam-3153	134	3	(	(	PUNCT
ejpam-3153	134	4	−1)nexn	−1)nexn	PROPN
ejpam-3153	134	5	.	.	PUNCT
ejpam-3153	135	1	(	(	PUNCT
ejpam-3153	135	2	29	29	NUM
ejpam-3153	135	3	)	)	PUNCT
ejpam-3153	135	4	proof	proof	NOUN
ejpam-3153	135	5	.	.	PUNCT
ejpam-3153	136	1	replacing	replace	VERB
ejpam-3153	136	2	t	t	PROPN
ejpam-3153	136	3	by	by	ADP
ejpam-3153	136	4	−it	−it	PROPN
ejpam-3153	136	5	,	,	PUNCT
ejpam-3153	136	6	where	where	SCONJ
ejpam-3153	136	7	i2	i2	PROPN
ejpam-3153	136	8	=	=	SYM
ejpam-3153	136	9	−1	−1	NOUN
ejpam-3153	136	10	in	in	ADP
ejpam-3153	136	11	the	the	DET
ejpam-3153	136	12	generating	generate	VERB
ejpam-3153	136	13	function	function	NOUN
ejpam-3153	136	14	of	of	ADP
ejpam-3153	136	15	ch	ch	NOUN
ejpam-3153	136	16	(	(	PUNCT
ejpam-3153	136	17	r	r	NOUN
ejpam-3153	136	18	)	)	PUNCT
ejpam-3153	136	19	n	n	NOUN
ejpam-3153	136	20	,	,	PUNCT
ejpam-3153	136	21	we	we	PRON
ejpam-3153	136	22	have	have	VERB
ejpam-3153	136	23	(	(	PUNCT
ejpam-3153	136	24	2	2	NUM
ejpam-3153	136	25	2−	2−	NUM
ejpam-3153	136	26	it	it	PRON
ejpam-3153	136	27	)	)	PUNCT
ejpam-3153	137	1	r	r	NOUN
ejpam-3153	137	2	=	=	PUNCT
ejpam-3153	137	3	∞∑	∞∑	NUM
ejpam-3153	137	4	n=0	n=0	NUM
ejpam-3153	137	5	ch(r	ch(r	NOUN
ejpam-3153	137	6	)	)	PUNCT
ejpam-3153	137	7	n	n	CCONJ
ejpam-3153	137	8	(	(	PUNCT
ejpam-3153	137	9	−it)n	−it)n	PROPN
ejpam-3153	137	10	n	n	CCONJ
ejpam-3153	137	11	!	!	NUM
ejpam-3153	137	12	,	,	PUNCT
ejpam-3153	137	13	(	(	PUNCT
ejpam-3153	137	14	30	30	X
ejpam-3153	137	15	)	)	PUNCT
ejpam-3153	137	16	the	the	DET
ejpam-3153	137	17	left	left	ADJ
ejpam-3153	137	18	-	-	PUNCT
ejpam-3153	137	19	hand	hand	NOUN
ejpam-3153	137	20	side	side	NOUN
ejpam-3153	137	21	of	of	ADP
ejpam-3153	137	22	eq.(30	eq.(30	NOUN
ejpam-3153	137	23	)	)	PUNCT
ejpam-3153	137	24	can	can	AUX
ejpam-3153	137	25	be	be	AUX
ejpam-3153	137	26	written	write	VERB
ejpam-3153	137	27	as	as	ADP
ejpam-3153	137	28	(	(	PUNCT
ejpam-3153	137	29	1−	1−	NUM
ejpam-3153	137	30	it	it	PRON
ejpam-3153	137	31	2	2	X
ejpam-3153	137	32	)	)	PUNCT
ejpam-3153	137	33	−r	−r	ADJ
ejpam-3153	137	34	=	=	NOUN
ejpam-3153	137	35	eeitx	eeitx	NOUN
ejpam-3153	137	36	=	=	X
ejpam-3153	137	37	∞∑	∞∑	NUM
ejpam-3153	137	38	n=0	n=0	PUNCT
ejpam-3153	137	39	exn	exn	NOUN
ejpam-3153	137	40	(	(	PUNCT
ejpam-3153	137	41	it)n	it)n	PROPN
ejpam-3153	137	42	n	n	NUM
ejpam-3153	137	43	!	!	PUNCT
ejpam-3153	137	44	,	,	PUNCT
ejpam-3153	137	45	(	(	PUNCT
ejpam-3153	137	46	31	31	NUM
ejpam-3153	137	47	)	)	PUNCT
ejpam-3153	137	48	from	from	ADP
ejpam-3153	137	49	eq.(30	eq.(30	NOUN
ejpam-3153	137	50	)	)	PUNCT
ejpam-3153	137	51	and	and	CCONJ
ejpam-3153	137	52	eq.(31	eq.(31	NOUN
ejpam-3153	137	53	)	)	PUNCT
ejpam-3153	137	54	,	,	PUNCT
ejpam-3153	137	55	we	we	PRON
ejpam-3153	137	56	obtain	obtain	VERB
ejpam-3153	137	57	∞∑	∞∑	NUM
ejpam-3153	137	58	n=0	n=0	NUM
ejpam-3153	137	59	ch(r	ch(r	NOUN
ejpam-3153	137	60	)	)	PUNCT
ejpam-3153	137	61	n	n	CCONJ
ejpam-3153	137	62	(	(	PUNCT
ejpam-3153	137	63	−it)n	−it)n	NOUN
ejpam-3153	137	64	n	n	CCONJ
ejpam-3153	137	65	!	!	PUNCT
ejpam-3153	137	66	=	=	NOUN
ejpam-3153	138	1	∞∑	∞∑	PRON
ejpam-3153	138	2	n=0	n=0	NUM
ejpam-3153	138	3	(	(	PUNCT
ejpam-3153	138	4	−1)nexn	−1)nexn	PROPN
ejpam-3153	138	5	(	(	PUNCT
ejpam-3153	138	6	−it)n	−it)n	PROPN
ejpam-3153	138	7	n	n	CCONJ
ejpam-3153	138	8	!	!	PUNCT
ejpam-3153	138	9	.	.	PUNCT
ejpam-3153	139	1	by	by	ADP
ejpam-3153	139	2	comparing	compare	VERB
ejpam-3153	139	3	the	the	DET
ejpam-3153	139	4	coefficients	coefficient	NOUN
ejpam-3153	139	5	of	of	ADP
ejpam-3153	139	6	(	(	PUNCT
ejpam-3153	139	7	−it)n	−it)n	PROPN
ejpam-3153	139	8	n	n	CCONJ
ejpam-3153	139	9	!	!	PROPN
ejpam-3153	139	10	,	,	PUNCT
ejpam-3153	139	11	theorem	theorem	VERB
ejpam-3153	139	12	7	7	NUM
ejpam-3153	139	13	is	be	AUX
ejpam-3153	139	14	proved	prove	VERB
ejpam-3153	139	15	.	.	PUNCT
ejpam-3153	140	1	theorem	theorem	ADJ
ejpam-3153	140	2	8	8	NUM
ejpam-3153	140	3	.	.	PUNCT
ejpam-3153	141	1	under	under	ADP
ejpam-3153	141	2	the	the	DET
ejpam-3153	141	3	circumstance	circumstance	NOUN
ejpam-3153	141	4	of	of	ADP
ejpam-3153	141	5	theorem	theorem	ADJ
ejpam-3153	141	6	7	7	NUM
ejpam-3153	141	7	,	,	PUNCT
ejpam-3153	141	8	higher	high	ADJ
ejpam-3153	141	9	-	-	PUNCT
ejpam-3153	141	10	order	order	NOUN
ejpam-3153	141	11	changhee	changhee	NOUN
ejpam-3153	141	12	polynomials	polynomial	NOUN
ejpam-3153	141	13	of	of	ADP
ejpam-3153	141	14	the	the	DET
ejpam-3153	141	15	second	second	ADJ
ejpam-3153	141	16	kind	kind	NOUN
ejpam-3153	141	17	ĉh	ĉh	X
ejpam-3153	141	18	(	(	PUNCT
ejpam-3153	141	19	r	r	NOUN
ejpam-3153	141	20	)	)	PUNCT
ejpam-3153	141	21	n	n	NOUN
ejpam-3153	141	22	(	(	PUNCT
ejpam-3153	141	23	x	x	X
ejpam-3153	141	24	)	)	PUNCT
ejpam-3153	141	25	satisfy	satisfy	PROPN
ejpam-3153	141	26	ĉh(r	ĉh(r	PROPN
ejpam-3153	141	27	)	)	PUNCT
ejpam-3153	141	28	n	n	CCONJ
ejpam-3153	141	29	(	(	PUNCT
ejpam-3153	141	30	x	x	X
ejpam-3153	141	31	)	)	PUNCT
ejpam-3153	142	1	=	=	SYM
ejpam-3153	142	2	n∑	n∑	NOUN
ejpam-3153	142	3	k=0	k=0	PROPN
ejpam-3153	142	4	(	(	PUNCT
ejpam-3153	142	5	n	n	X
ejpam-3153	142	6	k	k	NOUN
ejpam-3153	142	7	)	)	PUNCT
ejpam-3153	142	8	(	(	PUNCT
ejpam-3153	143	1	−1)k(x+	−1)k(x+	ADV
ejpam-3153	143	2	r)n−kex	r)n−kex	PROPN
ejpam-3153	143	3	k.	k.	PROPN
ejpam-3153	143	4	(	(	PUNCT
ejpam-3153	143	5	32	32	NUM
ejpam-3153	143	6	)	)	PUNCT
ejpam-3153	143	7	proof	proof	NOUN
ejpam-3153	143	8	.	.	PUNCT
ejpam-3153	144	1	the	the	DET
ejpam-3153	144	2	generating	generate	VERB
ejpam-3153	144	3	function	function	NOUN
ejpam-3153	144	4	of	of	ADP
ejpam-3153	144	5	ĉh	ĉh	NOUN
ejpam-3153	144	6	(	(	PUNCT
ejpam-3153	144	7	r	r	NOUN
ejpam-3153	144	8	)	)	PUNCT
ejpam-3153	144	9	n	n	NOUN
ejpam-3153	144	10	(	(	PUNCT
ejpam-3153	144	11	x	x	X
ejpam-3153	144	12	)	)	PUNCT
ejpam-3153	144	13	can	can	AUX
ejpam-3153	144	14	be	be	AUX
ejpam-3153	144	15	written	write	VERB
ejpam-3153	144	16	as	as	ADP
ejpam-3153	144	17	∞∑	∞∑	NUM
ejpam-3153	144	18	n=0	n=0	PROPN
ejpam-3153	144	19	ĉh(r	ĉh(r	NOUN
ejpam-3153	144	20	)	)	PUNCT
ejpam-3153	144	21	n	n	CCONJ
ejpam-3153	144	22	(	(	PUNCT
ejpam-3153	144	23	x	x	X
ejpam-3153	144	24	)	)	PUNCT
ejpam-3153	144	25	tn	tn	PROPN
ejpam-3153	144	26	n	n	NOUN
ejpam-3153	144	27	!	!	PUNCT
ejpam-3153	145	1	=	=	PUNCT
ejpam-3153	145	2	(	(	PUNCT
ejpam-3153	145	3	2	2	NUM
ejpam-3153	145	4	2	2	NUM
ejpam-3153	145	5	+	+	NUM
ejpam-3153	145	6	t	t	NOUN
ejpam-3153	145	7	)	)	PUNCT
ejpam-3153	145	8	r(1	r(1	PROPN
ejpam-3153	146	1	+	+	NUM
ejpam-3153	146	2	t)x+r	t)x+r	X
ejpam-3153	146	3	=	=	PUNCT
ejpam-3153	147	1	∞∑	∞∑	ADJ
ejpam-3153	147	2	n=0	n=0	NUM
ejpam-3153	147	3	(	(	PUNCT
ejpam-3153	147	4	−1)nexn	−1)nexn	PROPN
ejpam-3153	147	5	t	t	PROPN
ejpam-3153	147	6	n	n	PRON
ejpam-3153	147	7	n	n	CCONJ
ejpam-3153	147	8	!	!	PUNCT
ejpam-3153	148	1	∞∑	∞∑	NUM
ejpam-3153	148	2	n=0	n=0	NUM
ejpam-3153	148	3	(	(	PUNCT
ejpam-3153	148	4	x+	x+	X
ejpam-3153	148	5	r)n	r)n	X
ejpam-3153	148	6	tn	tn	NOUN
ejpam-3153	148	7	n	n	PROPN
ejpam-3153	148	8	!	!	PUNCT
ejpam-3153	148	9	c.	c.	PROPN
ejpam-3153	148	10	liu	liu	PROPN
ejpam-3153	148	11	,	,	PUNCT
ejpam-3153	148	12	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	148	13	/	/	SYM
ejpam-3153	148	14	eur	eur	PROPN
ejpam-3153	148	15	.	.	PUNCT
ejpam-3153	149	1	j.	j.	PROPN
ejpam-3153	149	2	pure	pure	PROPN
ejpam-3153	149	3	appl	appl	PROPN
ejpam-3153	149	4	.	.	PROPN
ejpam-3153	149	5	math	math	PROPN
ejpam-3153	149	6	,	,	PUNCT
ejpam-3153	149	7	11	11	NUM
ejpam-3153	149	8	(	(	PUNCT
ejpam-3153	149	9	1	1	NUM
ejpam-3153	149	10	)	)	PUNCT
ejpam-3153	149	11	(	(	PUNCT
ejpam-3153	149	12	2018	2018	NUM
ejpam-3153	149	13	)	)	PUNCT
ejpam-3153	149	14	,	,	PUNCT
ejpam-3153	149	15	69	69	NUM
ejpam-3153	149	16	-	-	SYM
ejpam-3153	149	17	78	78	NUM
ejpam-3153	149	18	76	76	NUM
ejpam-3153	149	19	=	=	NOUN
ejpam-3153	150	1	∞∑	∞∑	NUM
ejpam-3153	150	2	n=0	n=0	NUM
ejpam-3153	150	3	n∑	n∑	NOUN
ejpam-3153	150	4	k=0	k=0	PROPN
ejpam-3153	150	5	(	(	PUNCT
ejpam-3153	150	6	n	n	X
ejpam-3153	150	7	k	k	NOUN
ejpam-3153	150	8	)	)	PUNCT
ejpam-3153	150	9	(	(	PUNCT
ejpam-3153	150	10	−1)kexk(x+	−1)kexk(x+	ADP
ejpam-3153	150	11	r)n−k	r)n−k	NOUN
ejpam-3153	150	12	tn	tn	NOUN
ejpam-3153	150	13	n	n	X
ejpam-3153	150	14	!	!	PUNCT
ejpam-3153	150	15	.	.	PUNCT
ejpam-3153	151	1	by	by	ADP
ejpam-3153	151	2	comparing	compare	VERB
ejpam-3153	151	3	the	the	DET
ejpam-3153	151	4	coefficients	coefficient	NOUN
ejpam-3153	151	5	of	of	ADP
ejpam-3153	151	6	tn	tn	NOUN
ejpam-3153	151	7	n	n	CCONJ
ejpam-3153	151	8	!	!	PROPN
ejpam-3153	151	9	,	,	PUNCT
ejpam-3153	151	10	theorem	theorem	VERB
ejpam-3153	151	11	8	8	NUM
ejpam-3153	151	12	is	be	AUX
ejpam-3153	151	13	proved	prove	VERB
ejpam-3153	151	14	.	.	PUNCT
ejpam-3153	152	1	corollary	corollary	ADJ
ejpam-3153	152	2	6	6	NUM
ejpam-3153	152	3	.	.	PUNCT
ejpam-3153	153	1	in	in	ADP
ejpam-3153	153	2	theorem	theorem	NOUN
ejpam-3153	153	3	8	8	NUM
ejpam-3153	153	4	,	,	PUNCT
ejpam-3153	153	5	taking	take	VERB
ejpam-3153	153	6	x	x	PUNCT
ejpam-3153	153	7	=	=	SYM
ejpam-3153	153	8	0	0	NUM
ejpam-3153	153	9	,	,	PUNCT
ejpam-3153	153	10	we	we	PRON
ejpam-3153	153	11	obtain	obtain	VERB
ejpam-3153	153	12	the	the	DET
ejpam-3153	153	13	moment	moment	NOUN
ejpam-3153	153	14	form	form	NOUN
ejpam-3153	153	15	of	of	ADP
ejpam-3153	153	16	higher	high	ADJ
ejpam-3153	153	17	-	-	PUNCT
ejpam-3153	153	18	order	order	NOUN
ejpam-3153	153	19	changhee	changhee	NOUN
ejpam-3153	153	20	numbers	number	NOUN
ejpam-3153	153	21	of	of	ADP
ejpam-3153	153	22	the	the	DET
ejpam-3153	153	23	second	second	ADJ
ejpam-3153	153	24	kind	kind	NOUN
ejpam-3153	153	25	,	,	PUNCT
ejpam-3153	153	26	ĉh(r	ĉh(r	NOUN
ejpam-3153	153	27	)	)	PUNCT
ejpam-3153	153	28	n	n	PROPN
ejpam-3153	154	1	=	=	SYM
ejpam-3153	154	2	n∑	n∑	NOUN
ejpam-3153	154	3	k=0	k=0	PROPN
ejpam-3153	154	4	(	(	PUNCT
ejpam-3153	154	5	n	n	X
ejpam-3153	154	6	k	k	NOUN
ejpam-3153	154	7	)	)	PUNCT
ejpam-3153	154	8	(	(	PUNCT
ejpam-3153	154	9	−1)k(r)n−kex	−1)k(r)n−kex	PROPN
ejpam-3153	154	10	k.	k.	NOUN
ejpam-3153	154	11	(	(	PUNCT
ejpam-3153	154	12	33	33	NUM
ejpam-3153	154	13	)	)	PUNCT
ejpam-3153	154	14	corollary	corollary	NOUN
ejpam-3153	154	15	7	7	NUM
ejpam-3153	154	16	.	.	PUNCT
ejpam-3153	155	1	since	since	SCONJ
ejpam-3153	155	2	the	the	DET
ejpam-3153	155	3	generating	generate	VERB
ejpam-3153	155	4	function	function	NOUN
ejpam-3153	155	5	of	of	ADP
ejpam-3153	155	6	higher	high	ADJ
ejpam-3153	155	7	-	-	PUNCT
ejpam-3153	155	8	order	order	NOUN
ejpam-3153	155	9	changhee	changhee	NOUN
ejpam-3153	155	10	polynomials	polynomial	NOUN
ejpam-3153	155	11	is	be	AUX
ejpam-3153	155	12	∞∑	∞∑	NUM
ejpam-3153	155	13	n=0	n=0	NUM
ejpam-3153	155	14	ch(r	ch(r	NUM
ejpam-3153	155	15	)	)	PUNCT
ejpam-3153	155	16	n	n	CCONJ
ejpam-3153	155	17	(	(	PUNCT
ejpam-3153	155	18	x	x	X
ejpam-3153	155	19	)	)	PUNCT
ejpam-3153	155	20	tn	tn	PROPN
ejpam-3153	155	21	n	n	NOUN
ejpam-3153	155	22	!	!	PUNCT
ejpam-3153	156	1	=	=	PUNCT
ejpam-3153	156	2	(	(	PUNCT
ejpam-3153	156	3	2	2	NUM
ejpam-3153	156	4	t+	t+	NUM
ejpam-3153	156	5	2	2	NUM
ejpam-3153	156	6	)	)	PUNCT
ejpam-3153	156	7	r(1	r(1	PROPN
ejpam-3153	156	8	+	+	CCONJ
ejpam-3153	156	9	t)x	t)x	ADJ
ejpam-3153	156	10	.	.	PUNCT
ejpam-3153	157	1	(	(	PUNCT
ejpam-3153	157	2	34	34	NUM
ejpam-3153	157	3	)	)	PUNCT
ejpam-3153	157	4	from	from	ADP
ejpam-3153	157	5	theorem	theorem	ADJ
ejpam-3153	157	6	8	8	NUM
ejpam-3153	157	7	,	,	PUNCT
ejpam-3153	157	8	we	we	PRON
ejpam-3153	157	9	can	can	AUX
ejpam-3153	157	10	see	see	VERB
ejpam-3153	157	11	that	that	SCONJ
ejpam-3153	157	12	the	the	DET
ejpam-3153	157	13	moment	moment	NOUN
ejpam-3153	157	14	form	form	NOUN
ejpam-3153	157	15	of	of	ADP
ejpam-3153	157	16	ch	ch	NOUN
ejpam-3153	157	17	(	(	PUNCT
ejpam-3153	157	18	r	r	NOUN
ejpam-3153	157	19	)	)	PUNCT
ejpam-3153	157	20	n	n	NOUN
ejpam-3153	157	21	(	(	PUNCT
ejpam-3153	157	22	x	x	X
ejpam-3153	157	23	)	)	PUNCT
ejpam-3153	157	24	is	be	AUX
ejpam-3153	157	25	ch(r	ch(r	PRON
ejpam-3153	157	26	)	)	PUNCT
ejpam-3153	158	1	n	n	CCONJ
ejpam-3153	158	2	(	(	PUNCT
ejpam-3153	158	3	x	x	X
ejpam-3153	158	4	)	)	PUNCT
ejpam-3153	158	5	=	=	SYM
ejpam-3153	159	1	n∑	n∑	NOUN
ejpam-3153	159	2	k=0	k=0	PROPN
ejpam-3153	159	3	(	(	PUNCT
ejpam-3153	159	4	n	n	X
ejpam-3153	159	5	k	k	NOUN
ejpam-3153	159	6	)	)	PUNCT
ejpam-3153	159	7	(	(	PUNCT
ejpam-3153	159	8	−1)k(x)n−kex	−1)k(x)n−kex	PROPN
ejpam-3153	159	9	k.	k.	NOUN
ejpam-3153	159	10	(	(	PUNCT
ejpam-3153	159	11	35	35	NUM
ejpam-3153	159	12	)	)	PUNCT
ejpam-3153	159	13	3	3	NUM
ejpam-3153	159	14	.	.	X
ejpam-3153	160	1	identities	identity	NOUN
ejpam-3153	160	2	of	of	ADP
ejpam-3153	160	3	daehee	daehee	NOUN
ejpam-3153	160	4	numbers	number	NOUN
ejpam-3153	160	5	and	and	CCONJ
ejpam-3153	160	6	special	special	ADJ
ejpam-3153	160	7	combinatorial	combinatorial	ADJ
ejpam-3153	160	8	sequences	sequence	NOUN
ejpam-3153	160	9	in	in	ADP
ejpam-3153	160	10	this	this	DET
ejpam-3153	160	11	section	section	NOUN
ejpam-3153	160	12	,	,	PUNCT
ejpam-3153	160	13	we	we	PRON
ejpam-3153	160	14	use	use	VERB
ejpam-3153	160	15	moment	moment	NOUN
ejpam-3153	160	16	forms	form	NOUN
ejpam-3153	160	17	of	of	ADP
ejpam-3153	160	18	special	special	ADJ
ejpam-3153	160	19	combinatorial	combinatorial	ADJ
ejpam-3153	160	20	sequences	sequence	NOUN
ejpam-3153	160	21	,	,	PUNCT
ejpam-3153	160	22	characteristic	characteristic	ADJ
ejpam-3153	160	23	function	function	NOUN
ejpam-3153	160	24	and	and	CCONJ
ejpam-3153	160	25	generating	generate	VERB
ejpam-3153	160	26	function	function	NOUN
ejpam-3153	160	27	method	method	NOUN
ejpam-3153	160	28	to	to	PART
ejpam-3153	160	29	investigate	investigate	VERB
ejpam-3153	160	30	the	the	DET
ejpam-3153	160	31	relationships	relationship	NOUN
ejpam-3153	160	32	between	between	ADP
ejpam-3153	160	33	daehee	daehee	NOUN
ejpam-3153	160	34	numbers	number	NOUN
ejpam-3153	160	35	dn	dn	VERB
ejpam-3153	160	36	,	,	PUNCT
ejpam-3153	160	37	cauchy	cauchy	ADJ
ejpam-3153	160	38	numbers	number	NOUN
ejpam-3153	160	39	of	of	ADP
ejpam-3153	160	40	the	the	DET
ejpam-3153	160	41	second	second	ADJ
ejpam-3153	160	42	kind	kind	NOUN
ejpam-3153	160	43	ĉn	ĉn	NOUN
ejpam-3153	160	44	,	,	PUNCT
ejpam-3153	160	45	derangement	derangement	NOUN
ejpam-3153	160	46	numbers	number	NOUN
ejpam-3153	160	47	dn	dn	VERB
ejpam-3153	160	48	,	,	PUNCT
ejpam-3153	160	49	and	and	CCONJ
ejpam-3153	160	50	stirling	stirling	NOUN
ejpam-3153	160	51	numbers	number	NOUN
ejpam-3153	160	52	of	of	ADP
ejpam-3153	160	53	the	the	DET
ejpam-3153	160	54	first	first	ADJ
ejpam-3153	160	55	kind	kind	NOUN
ejpam-3153	160	56	,	,	PUNCT
ejpam-3153	160	57	then	then	ADV
ejpam-3153	160	58	we	we	PRON
ejpam-3153	160	59	obtain	obtain	VERB
ejpam-3153	160	60	combinatorial	combinatorial	ADJ
ejpam-3153	160	61	identities	identity	NOUN
ejpam-3153	160	62	about	about	ADP
ejpam-3153	160	63	them	they	PRON
ejpam-3153	160	64	.	.	PUNCT
ejpam-3153	161	1	theorem	theorem	VERB
ejpam-3153	161	2	9	9	NUM
ejpam-3153	161	3	.	.	PUNCT
ejpam-3153	162	1	let	let	VERB
ejpam-3153	162	2	r.v	r.v	PRON
ejpam-3153	162	3	u	u	NOUN
ejpam-3153	162	4	∼	∼	NOUN
ejpam-3153	162	5	u	u	NOUN
ejpam-3153	162	6	[	[	X
ejpam-3153	162	7	0	0	NUM
ejpam-3153	162	8	,	,	PUNCT
ejpam-3153	162	9	1	1	NUM
ejpam-3153	162	10	]	]	PUNCT
ejpam-3153	162	11	,	,	PUNCT
ejpam-3153	162	12	γ	γ	X
ejpam-3153	162	13	∼	∼	NOUN
ejpam-3153	162	14	γ(1	γ(1	PROPN
ejpam-3153	162	15	,	,	PUNCT
ejpam-3153	162	16	1	1	NUM
ejpam-3153	162	17	)	)	PUNCT
ejpam-3153	162	18	,	,	PUNCT
ejpam-3153	162	19	x	x	X
ejpam-3153	162	20	∼	∼	NOUN
ejpam-3153	162	21	γ(u	γ(u	NOUN
ejpam-3153	162	22	,	,	PUNCT
ejpam-3153	162	23	1	1	NUM
ejpam-3153	162	24	)	)	PUNCT
ejpam-3153	162	25	,	,	PUNCT
ejpam-3153	162	26	then	then	ADV
ejpam-3153	162	27	daehee	daehee	NOUN
ejpam-3153	162	28	numbers	number	NOUN
ejpam-3153	162	29	dn	dn	VERB
ejpam-3153	162	30	,	,	PUNCT
ejpam-3153	162	31	cauchy	cauchy	ADJ
ejpam-3153	162	32	numbers	number	NOUN
ejpam-3153	162	33	of	of	ADP
ejpam-3153	162	34	the	the	DET
ejpam-3153	162	35	second	second	ADJ
ejpam-3153	162	36	kind	kind	NOUN
ejpam-3153	162	37	ĉn	ĉn	NOUN
ejpam-3153	162	38	,	,	PUNCT
ejpam-3153	162	39	and	and	CCONJ
ejpam-3153	162	40	derangement	derangement	NOUN
ejpam-3153	162	41	numbers	number	NOUN
ejpam-3153	162	42	dn	dn	PART
ejpam-3153	162	43	satisfy	satisfy	VERB
ejpam-3153	162	44	the	the	DET
ejpam-3153	162	45	following	follow	VERB
ejpam-3153	162	46	identity	identity	NOUN
ejpam-3153	163	1	n∑	n∑	NOUN
ejpam-3153	163	2	k=0	k=0	PROPN
ejpam-3153	163	3	(	(	PUNCT
ejpam-3153	163	4	n	n	X
ejpam-3153	163	5	k	k	NOUN
ejpam-3153	163	6	)	)	PUNCT
ejpam-3153	163	7	(	(	PUNCT
ejpam-3153	163	8	−1)ndkĉn−k	−1)ndkĉn−k	NOUN
ejpam-3153	163	9	=	=	SYM
ejpam-3153	163	10	n∑	n∑	NOUN
ejpam-3153	163	11	k=0	k=0	PROPN
ejpam-3153	163	12	(	(	PUNCT
ejpam-3153	163	13	n	n	X
ejpam-3153	163	14	k	k	NOUN
ejpam-3153	163	15	)	)	PUNCT
ejpam-3153	163	16	dk	dk	PROPN
ejpam-3153	163	17	,	,	PUNCT
ejpam-3153	163	18	n	n	X
ejpam-3153	163	19	>	>	X
ejpam-3153	163	20	0	0	NUM
ejpam-3153	163	21	.	.	PUNCT
ejpam-3153	164	1	(	(	PUNCT
ejpam-3153	164	2	36	36	NUM
ejpam-3153	164	3	)	)	PUNCT
ejpam-3153	164	4	proof	proof	NOUN
ejpam-3153	164	5	.	.	PUNCT
ejpam-3153	165	1	on	on	ADP
ejpam-3153	165	2	one	one	NUM
ejpam-3153	165	3	hand	hand	NOUN
ejpam-3153	165	4	,	,	PUNCT
ejpam-3153	165	5	[	[	X
ejpam-3153	165	6	e(uγ)−	e(uγ)−	ADJ
ejpam-3153	165	7	ex]n	ex]n	PROPN
ejpam-3153	165	8	=	=	SYM
ejpam-3153	165	9	n∑	n∑	NOUN
ejpam-3153	165	10	k=0	k=0	PROPN
ejpam-3153	165	11	(	(	PUNCT
ejpam-3153	165	12	n	n	X
ejpam-3153	165	13	k	k	NOUN
ejpam-3153	165	14	)	)	PUNCT
ejpam-3153	165	15	e(uγ)k(−ex)n−k	e(uγ)k(−ex)n−k	PUNCT
ejpam-3153	166	1	=	=	PUNCT
ejpam-3153	166	2	n∑	n∑	NOUN
ejpam-3153	166	3	k=0	k=0	PROPN
ejpam-3153	166	4	(	(	PUNCT
ejpam-3153	166	5	n	n	X
ejpam-3153	166	6	k	k	NOUN
ejpam-3153	166	7	)	)	PUNCT
ejpam-3153	166	8	(	(	PUNCT
ejpam-3153	166	9	−1)ne(−uγ)kexn−k	−1)ne(−uγ)kexn−k	PROPN
ejpam-3153	166	10	c.	c.	PROPN
ejpam-3153	166	11	liu	liu	PROPN
ejpam-3153	166	12	,	,	PUNCT
ejpam-3153	166	13	wuyungaowa	wuyungaowa	PROPN
ejpam-3153	166	14	/	/	SYM
ejpam-3153	166	15	eur	eur	PROPN
ejpam-3153	166	16	.	.	PUNCT
ejpam-3153	167	1	j.	j.	PROPN
ejpam-3153	167	2	pure	pure	PROPN
ejpam-3153	167	3	appl	appl	PROPN
ejpam-3153	167	4	.	.	PROPN
ejpam-3153	167	5	math	math	PROPN
ejpam-3153	167	6	,	,	PUNCT
ejpam-3153	167	7	11	11	NUM
ejpam-3153	167	8	(	(	PUNCT
ejpam-3153	167	9	1	1	NUM
ejpam-3153	167	10	)	)	PUNCT
ejpam-3153	167	11	(	(	PUNCT
ejpam-3153	167	12	2018	2018	NUM
ejpam-3153	167	13	)	)	PUNCT
ejpam-3153	167	14	,	,	PUNCT
ejpam-3153	167	15	69	69	NUM
ejpam-3153	167	16	-	-	SYM
ejpam-3153	167	17	78	78	NUM
ejpam-3153	167	18	77	77	NUM
ejpam-3153	167	19	=	=	SYM
ejpam-3153	167	20	n∑	n∑	NOUN
ejpam-3153	167	21	k=0	k=0	PROPN
ejpam-3153	167	22	(	(	PUNCT
ejpam-3153	167	23	n	n	X
ejpam-3153	167	24	k	k	NOUN
ejpam-3153	167	25	)	)	PUNCT
ejpam-3153	167	26	(	(	PUNCT
ejpam-3153	167	27	−1)ndkĉn−k	−1)ndkĉn−k	PROPN
ejpam-3153	167	28	,	,	PUNCT
ejpam-3153	167	29	(	(	PUNCT
ejpam-3153	167	30	37	37	NUM
ejpam-3153	167	31	)	)	PUNCT
ejpam-3153	167	32	write	write	VERB
ejpam-3153	167	33	the	the	DET
ejpam-3153	167	34	generating	generate	VERB
ejpam-3153	167	35	function	function	NOUN
ejpam-3153	167	36	of	of	ADP
ejpam-3153	167	37	the	the	DET
ejpam-3153	167	38	equation	equation	NOUN
ejpam-3153	167	39	above	above	ADV
ejpam-3153	167	40	,	,	PUNCT
ejpam-3153	167	41	noting	note	VERB
ejpam-3153	167	42	that	that	SCONJ
ejpam-3153	167	43	i2	i2	PROPN
ejpam-3153	167	44	=	=	PUNCT
ejpam-3153	167	45	−1	−1	NOUN
ejpam-3153	167	46	∞∑	∞∑	NOUN
ejpam-3153	167	47	n=0	n=0	PUNCT
ejpam-3153	167	48	[	[	X
ejpam-3153	167	49	e(uγ)−	e(uγ)−	NOUN
ejpam-3153	167	50	ex]n	ex]n	PROPN
ejpam-3153	167	51	(	(	PUNCT
ejpam-3153	167	52	it)n	it)n	PROPN
ejpam-3153	167	53	n	n	NOUN
ejpam-3153	167	54	!	!	PUNCT
ejpam-3153	167	55	=	=	NOUN
ejpam-3153	168	1	∞∑	∞∑	PRON
ejpam-3153	168	2	n=0	n=0	NUM
ejpam-3153	168	3	n∑	n∑	NOUN
ejpam-3153	168	4	k=0	k=0	PROPN
ejpam-3153	168	5	(	(	PUNCT
ejpam-3153	168	6	n	n	X
ejpam-3153	168	7	k	k	NOUN
ejpam-3153	168	8	)	)	PUNCT
ejpam-3153	168	9	(	(	PUNCT
ejpam-3153	168	10	−1)ndkĉn−k	−1)ndkĉn−k	X
ejpam-3153	168	11	(	(	PUNCT
ejpam-3153	168	12	it)n	it)n	PROPN
ejpam-3153	168	13	n	n	NOUN
ejpam-3153	168	14	!	!	PUNCT
ejpam-3153	168	15	=	=	NOUN
ejpam-3153	169	1	∞∑	∞∑	DET
ejpam-3153	169	2	n=0	n=0	NUM
ejpam-3153	169	3	dn	dn	NOUN
ejpam-3153	169	4	(	(	PUNCT
ejpam-3153	169	5	−it)n	−it)n	NOUN
ejpam-3153	169	6	n	n	CCONJ
ejpam-3153	169	7	!	!	PUNCT
ejpam-3153	170	1	∞∑	∞∑	NUM
ejpam-3153	170	2	n=0	n=0	NUM
ejpam-3153	170	3	ĉn	ĉn	NOUN
ejpam-3153	170	4	(	(	PUNCT
ejpam-3153	170	5	−it)n	−it)n	NOUN
ejpam-3153	170	6	n	n	CCONJ
ejpam-3153	170	7	!	!	PUNCT
ejpam-3153	170	8	=	=	PUNCT
ejpam-3153	171	1	ln(1−	ln(1−	PROPN
ejpam-3153	171	2	it	it	PRON
ejpam-3153	171	3	)	)	PUNCT
ejpam-3153	171	4	−it	−it	PROPN
ejpam-3153	171	5	−it	−it	PROPN
ejpam-3153	171	6	(	(	PUNCT
ejpam-3153	171	7	1−	1−	NUM
ejpam-3153	171	8	it	it	PRON
ejpam-3153	171	9	)	)	PUNCT
ejpam-3153	172	1	ln(1−	ln(1−	PROPN
ejpam-3153	172	2	it	it	PRON
ejpam-3153	172	3	)	)	PUNCT
ejpam-3153	172	4	=	=	SYM
ejpam-3153	172	5	eeitγ	eeitγ	NOUN
ejpam-3153	172	6	=	=	X
ejpam-3153	173	1	∞∑	∞∑	PRON
ejpam-3153	173	2	n=0	n=0	ADJ
ejpam-3153	173	3	eγn	eγn	NOUN
ejpam-3153	173	4	(	(	PUNCT
ejpam-3153	173	5	it)n	it)n	PROPN
ejpam-3153	173	6	n	n	NUM
ejpam-3153	173	7	!	!	PUNCT
ejpam-3153	173	8	,	,	PUNCT
ejpam-3153	173	9	(	(	PUNCT
ejpam-3153	173	10	38	38	NUM
ejpam-3153	173	11	)	)	PUNCT
ejpam-3153	173	12	on	on	ADP
ejpam-3153	173	13	the	the	DET
ejpam-3153	173	14	other	other	ADJ
ejpam-3153	173	15	hand	hand	NOUN
ejpam-3153	173	16	,	,	PUNCT
ejpam-3153	173	17	by	by	ADP
ejpam-3153	173	18	comparing	compare	VERB
ejpam-3153	173	19	the	the	DET
ejpam-3153	173	20	coefficients	coefficient	NOUN
ejpam-3153	173	21	of	of	ADP
ejpam-3153	173	22	(	(	PUNCT
ejpam-3153	173	23	it)n	it)n	PROPN
ejpam-3153	173	24	n	n	NOUN
ejpam-3153	173	25	!	!	PUNCT
ejpam-3153	173	26	in	in	ADP
ejpam-3153	173	27	eq.(38	eq.(38	NOUN
ejpam-3153	173	28	)	)	PUNCT
ejpam-3153	173	29	,	,	PUNCT
ejpam-3153	173	30	we	we	PRON
ejpam-3153	173	31	have	have	VERB
ejpam-3153	173	32	[	[	X
ejpam-3153	173	33	e(uγ)−	e(uγ)−	NOUN
ejpam-3153	173	34	ex]n	ex]n	NOUN
ejpam-3153	173	35	=	=	SYM
ejpam-3153	173	36	eγn	eγn	NOUN
ejpam-3153	173	37	=	=	SYM
ejpam-3153	173	38	e(γ−	e(γ−	PROPN
ejpam-3153	173	39	1	1	NUM
ejpam-3153	173	40	+	+	CCONJ
ejpam-3153	173	41	1)n	1)n	X
ejpam-3153	173	42	=	=	SYM
ejpam-3153	173	43	n∑	n∑	NOUN
ejpam-3153	173	44	k=0	k=0	PROPN
ejpam-3153	173	45	(	(	PUNCT
ejpam-3153	173	46	n	n	X
ejpam-3153	173	47	k	k	NOUN
ejpam-3153	173	48	)	)	PUNCT
ejpam-3153	173	49	e(γ−	e(γ−	PROPN
ejpam-3153	173	50	1)k	1)k	NUM
ejpam-3153	173	51	=	=	SYM
ejpam-3153	173	52	n∑	n∑	NOUN
ejpam-3153	173	53	k=0	k=0	PROPN
ejpam-3153	174	1	(	(	PUNCT
ejpam-3153	174	2	n	n	X
ejpam-3153	174	3	k	k	NOUN
ejpam-3153	174	4	)	)	PUNCT
ejpam-3153	174	5	dk	dk	PROPN
ejpam-3153	174	6	.	.	PUNCT
ejpam-3153	174	7	(	(	PUNCT
ejpam-3153	174	8	39	39	NUM
ejpam-3153	174	9	)	)	PUNCT
ejpam-3153	174	10	from	from	ADP
ejpam-3153	174	11	eq.(37	eq.(37	PROPN
ejpam-3153	174	12	)	)	PUNCT
ejpam-3153	174	13	and	and	CCONJ
ejpam-3153	174	14	eq.(39	eq.(39	ADJ
ejpam-3153	174	15	)	)	PUNCT
ejpam-3153	174	16	,	,	PUNCT
ejpam-3153	174	17	we	we	PRON
ejpam-3153	174	18	can	can	AUX
ejpam-3153	174	19	get	get	VERB
ejpam-3153	174	20	eq.(36	eq.(36	NOUN
ejpam-3153	174	21	)	)	PUNCT
ejpam-3153	174	22	.	.	PUNCT
ejpam-3153	175	1	theorem	theorem	NOUN
ejpam-3153	175	2	9	9	NUM
ejpam-3153	175	3	is	be	AUX
ejpam-3153	175	4	proved	prove	VERB
ejpam-3153	175	5	.	.	PUNCT
ejpam-3153	176	1	theorem	theorem	ADJ
ejpam-3153	176	2	10	10	NUM
ejpam-3153	176	3	.	.	PUNCT
ejpam-3153	177	1	higher	high	ADJ
ejpam-3153	177	2	-	-	PUNCT
ejpam-3153	177	3	order	order	NOUN
ejpam-3153	177	4	deahee	deahee	NOUN
ejpam-3153	177	5	numbers	number	NOUN
ejpam-3153	177	6	d	d	X
ejpam-3153	177	7	(	(	PUNCT
ejpam-3153	177	8	k	k	NOUN
ejpam-3153	177	9	)	)	PUNCT
ejpam-3153	177	10	n	n	NOUN
ejpam-3153	177	11	and	and	CCONJ
ejpam-3153	177	12	stirling	stirling	NOUN
ejpam-3153	177	13	numbers	number	NOUN
ejpam-3153	177	14	of	of	ADP
ejpam-3153	177	15	the	the	DET
ejpam-3153	177	16	first	first	ADJ
ejpam-3153	177	17	kind	kind	NOUN
ejpam-3153	177	18	satisfy	satisfy	VERB
ejpam-3153	177	19	the	the	DET
ejpam-3153	177	20	following	follow	VERB
ejpam-3153	177	21	relationship	relationship	NOUN
ejpam-3153	177	22	d(k	d(k	PROPN
ejpam-3153	177	23	)	)	PUNCT
ejpam-3153	178	1	n	n	PROPN
ejpam-3153	178	2	=	=	SYM
ejpam-3153	178	3	s(n+	s(n+	X
ejpam-3153	179	1	k	k	X
ejpam-3153	179	2	,	,	PUNCT
ejpam-3153	179	3	k	k	NOUN
ejpam-3153	179	4	)	)	PUNCT
ejpam-3153	179	5	(	(	PUNCT
ejpam-3153	179	6	n+k	n+k	PROPN
ejpam-3153	179	7	k	k	PROPN
ejpam-3153	179	8	)	)	PUNCT
ejpam-3153	179	9	.	.	PUNCT
ejpam-3153	180	1	(	(	PUNCT
ejpam-3153	180	2	40	40	NUM
ejpam-3153	180	3	)	)	PUNCT
ejpam-3153	180	4	proof	proof	NOUN
ejpam-3153	180	5	.	.	PUNCT
ejpam-3153	181	1	from	from	ADP
ejpam-3153	181	2	corollary	corollary	ADJ
ejpam-3153	181	3	1	1	NUM
ejpam-3153	181	4	and	and	CCONJ
ejpam-3153	181	5	lemma	lemma	PROPN
ejpam-3153	181	6	3	3	NUM
ejpam-3153	181	7	,	,	PUNCT
ejpam-3153	181	8	write	write	VERB
ejpam-3153	181	9	generating	generating	NOUN
ejpam-3153	181	10	function	function	NOUN
ejpam-3153	181	11	of	of	ADP
ejpam-3153	181	12	the	the	DET
ejpam-3153	181	13	left	left	ADJ
ejpam-3153	181	14	-	-	PUNCT
ejpam-3153	181	15	hand	hand	NOUN
ejpam-3153	181	16	side	side	NOUN
ejpam-3153	181	17	of	of	ADP
ejpam-3153	181	18	eq.(40	eq.(40	NOUN
ejpam-3153	181	19	)	)	PUNCT
ejpam-3153	181	20	,	,	PUNCT
ejpam-3153	181	21	∞∑	∞∑	PROPN
ejpam-3153	181	22	n=0	n=0	PROPN
ejpam-3153	181	23	d(k	d(k	PROPN
ejpam-3153	181	24	)	)	PUNCT
ejpam-3153	181	25	n	n	PROPN
ejpam-3153	181	26	tn	tn	NOUN
ejpam-3153	181	27	n	n	ADV
ejpam-3153	181	28	!	!	PUNCT
ejpam-3153	182	1	=	=	NOUN
ejpam-3153	183	1	∞∑	∞∑	PRON
ejpam-3153	183	2	n=0	n=0	NUM
ejpam-3153	183	3	(	(	PUNCT
ejpam-3153	183	4	−1)ne(u1γ1	−1)ne(u1γ1	NOUN
ejpam-3153	183	5	+	+	NUM
ejpam-3153	183	6	·	·	PUNCT
ejpam-3153	183	7	·	·	PUNCT
ejpam-3153	183	8	·	·	PUNCT
ejpam-3153	183	9	+	+	NUM
ejpam-3153	183	10	ukγk	ukγk	X
ejpam-3153	183	11	)	)	PUNCT
ejpam-3153	183	12	n	n	ADP
ejpam-3153	183	13	t	t	PROPN
ejpam-3153	183	14	n	n	NOUN
ejpam-3153	183	15	n	n	CCONJ
ejpam-3153	183	16	!	!	PUNCT
ejpam-3153	183	17	=	=	NOUN
ejpam-3153	184	1	∞∑	∞∑	PRON
ejpam-3153	184	2	n=0	n=0	NUM
ejpam-3153	184	3	(	(	PUNCT
ejpam-3153	184	4	−1)n	−1)n	X
ejpam-3153	184	5	(	(	PUNCT
ejpam-3153	184	6	n+	n+	NUM
ejpam-3153	184	7	k	k	X
ejpam-3153	184	8	k	k	X
ejpam-3153	184	9	)	)	PUNCT
ejpam-3153	184	10	e(u1γ1	e(u1γ1	PROPN
ejpam-3153	184	11	+	+	CCONJ
ejpam-3153	184	12	·	·	PUNCT
ejpam-3153	184	13	·	·	PUNCT
ejpam-3153	184	14	·	·	PUNCT
ejpam-3153	184	15	+	+	NUM
ejpam-3153	184	16	ukγk	ukγk	ADJ
ejpam-3153	184	17	)	)	PUNCT
ejpam-3153	184	18	nk	nk	PROPN
ejpam-3153	184	19	!	!	PROPN
ejpam-3153	184	20	tk	tk	PROPN
ejpam-3153	185	1	tn+k	tn+k	PROPN
ejpam-3153	185	2	(	(	PUNCT
ejpam-3153	185	3	n+	n+	NOUN
ejpam-3153	185	4	k	k	NOUN
ejpam-3153	185	5	)	)	PUNCT
ejpam-3153	185	6	!	!	PUNCT
ejpam-3153	186	1	=	=	PUNCT
ejpam-3153	187	1	∞∑	∞∑	PRON
ejpam-3153	187	2	n=0	n=0	NUM
ejpam-3153	187	3	s(n+	s(n+	NOUN
ejpam-3153	187	4	k	k	X
ejpam-3153	187	5	,	,	PUNCT
ejpam-3153	187	6	k	k	NOUN
ejpam-3153	187	7	)	)	PUNCT
ejpam-3153	187	8	(	(	PUNCT
ejpam-3153	187	9	n+k	n+k	PROPN
ejpam-3153	187	10	k	k	X
ejpam-3153	187	11	)	)	PUNCT
ejpam-3153	187	12	tn	tn	PROPN
ejpam-3153	187	13	n	n	PROPN
ejpam-3153	187	14	!	!	PUNCT
ejpam-3153	187	15	.	.	PUNCT
ejpam-3153	188	1	by	by	ADP
ejpam-3153	188	2	comparing	compare	VERB
ejpam-3153	188	3	the	the	DET
ejpam-3153	188	4	coefficients	coefficient	NOUN
ejpam-3153	188	5	of	of	ADP
ejpam-3153	188	6	tn	tn	NOUN
ejpam-3153	188	7	n	n	CCONJ
ejpam-3153	188	8	!	!	PROPN
ejpam-3153	188	9	,	,	PUNCT
ejpam-3153	188	10	we	we	PRON
ejpam-3153	188	11	obtain	obtain	VERB
ejpam-3153	188	12	the	the	DET
ejpam-3153	188	13	conclusion	conclusion	NOUN
ejpam-3153	188	14	.	.	PUNCT
ejpam-3153	189	1	references	reference	NOUN
ejpam-3153	189	2	78	78	NUM
ejpam-3153	189	3	acknowledgements	acknowledgement	NOUN
ejpam-3153	189	4	the	the	DET
ejpam-3153	189	5	research	research	NOUN
ejpam-3153	189	6	is	be	AUX
ejpam-3153	189	7	supported	support	VERB
ejpam-3153	189	8	by	by	ADP
ejpam-3153	189	9	the	the	DET
ejpam-3153	189	10	natural	natural	ADJ
ejpam-3153	189	11	science	science	PROPN
ejpam-3153	189	12	foundation	foundation	PROPN
ejpam-3153	189	13	of	of	ADP
ejpam-3153	189	14	china	china	PROPN
ejpam-3153	189	15	under	under	ADP
ejpam-3153	189	16	grant	grant	PROPN
ejpam-3153	189	17	11461050	11461050	NUM
ejpam-3153	189	18	and	and	CCONJ
ejpam-3153	189	19	natural	natural	ADJ
ejpam-3153	189	20	science	science	NOUN
ejpam-3153	189	21	foundation	foundation	NOUN
ejpam-3153	189	22	of	of	ADP
ejpam-3153	189	23	inner	inner	PROPN
ejpam-3153	189	24	mongolia	mongolia	PROPN
ejpam-3153	189	25	under	under	ADP
ejpam-3153	189	26	grant	grant	NOUN
ejpam-3153	189	27	2016ms0104	2016ms0104	NUM
ejpam-3153	189	28	references	reference	NOUN
ejpam-3153	189	29	[	[	X
ejpam-3153	189	30	1	1	NUM
ejpam-3153	189	31	]	]	PUNCT
ejpam-3153	189	32	jj	jj	PROPN
ejpam-3153	189	33	seo	seo	PROPN
ejpam-3153	189	34	ds	ds	PROPN
ejpam-3153	189	35	kim	kim	PROPN
ejpam-3153	189	36	,	,	PUNCT
ejpam-3153	189	37	t	t	PROPN
ejpam-3153	189	38	kim	kim	PROPN
ejpam-3153	189	39	and	and	CCONJ
ejpam-3153	189	40	sh	sh	PROPN
ejpam-3153	189	41	lee	lee	PROPN
ejpam-3153	189	42	.	.	PUNCT
ejpam-3153	190	1	higher	high	ADJ
ejpam-3153	190	2	-	-	PUNCT
ejpam-3153	190	3	order	order	NOUN
ejpam-3153	190	4	changhee	changhee	NOUN
ejpam-3153	190	5	numbers	number	NOUN
ejpam-3153	190	6	and	and	CCONJ
ejpam-3153	190	7	polynomials	polynomial	NOUN
ejpam-3153	190	8	.	.	PUNCT
ejpam-3153	191	1	adv	adv	PROPN
ejpam-3153	191	2	.	.	PUNCT
ejpam-3153	192	1	studies	study	NOUN
ejpam-3153	192	2	theor	theor	PROPN
ejpam-3153	192	3	.	.	PUNCT
ejpam-3153	193	1	phys	phy	NOUN
ejpam-3153	193	2	.	.	PUNCT
ejpam-3153	193	3	,	,	PUNCT
ejpam-3153	193	4	8(8):365–373	8(8):365–373	PROPN
ejpam-3153	193	5	,	,	PUNCT
ejpam-3153	193	6	2014	2014	NUM
ejpam-3153	193	7	.	.	PUNCT
ejpam-3153	194	1	[	[	X
ejpam-3153	194	2	2	2	X
ejpam-3153	194	3	]	]	X
ejpam-3153	194	4	sh	sh	PROPN
ejpam-3153	194	5	lee	lee	PROPN
ejpam-3153	194	6	ds	ds	PROPN
ejpam-3153	194	7	kim	kim	PROPN
ejpam-3153	194	8	,	,	PUNCT
ejpam-3153	194	9	t	t	PROPN
ejpam-3153	194	10	kim	kim	PROPN
ejpam-3153	194	11	and	and	CCONJ
ejpam-3153	194	12	jj	jj	PROPN
ejpam-3153	194	13	seo	seo	PROPN
ejpam-3153	194	14	.	.	PUNCT
ejpam-3153	195	1	a	a	DET
ejpam-3153	195	2	note	note	NOUN
ejpam-3153	195	3	on	on	ADP
ejpam-3153	195	4	the	the	DET
ejpam-3153	195	5	twisted	twisted	ADJ
ejpam-3153	195	6	lambda	lambda	NOUN
ejpam-3153	195	7	-	-	PUNCT
ejpam-3153	195	8	daehee	daehee	NOUN
ejpam-3153	195	9	polynomials	polynomial	NOUN
ejpam-3153	195	10	.	.	PUNCT
ejpam-3153	196	1	applied	apply	VERB
ejpam-3153	196	2	mathmetical	mathmetical	ADJ
ejpam-3153	196	3	sciences	science	NOUN
ejpam-3153	196	4	,	,	PUNCT
ejpam-3153	196	5	7(141):7005–7014	7(141):7005–7014	NUM
ejpam-3153	196	6	,	,	PUNCT
ejpam-3153	196	7	2013	2013	NUM
ejpam-3153	196	8	.	.	PUNCT
ejpam-3153	197	1	[	[	X
ejpam-3153	197	2	3	3	X
ejpam-3153	197	3	]	]	X
ejpam-3153	197	4	sh	sh	PROPN
ejpam-3153	197	5	lee	lee	PROPN
ejpam-3153	197	6	ds	ds	PROPN
ejpam-3153	197	7	kim	kim	PROPN
ejpam-3153	197	8	,	,	PUNCT
ejpam-3153	197	9	t	t	PROPN
ejpam-3153	197	10	kim	kim	PROPN
ejpam-3153	197	11	and	and	CCONJ
ejpam-3153	197	12	jj	jj	PROPN
ejpam-3153	197	13	seo	seo	PROPN
ejpam-3153	197	14	.	.	PUNCT
ejpam-3153	198	1	higher	high	ADJ
ejpam-3153	198	2	-	-	PUNCT
ejpam-3153	198	3	order	order	NOUN
ejpam-3153	198	4	daehee	daehee	NOUN
ejpam-3153	198	5	numbers	number	NOUN
ejpam-3153	198	6	and	and	CCONJ
ejpam-3153	198	7	polynomials	polynomial	NOUN
ejpam-3153	198	8	.	.	PUNCT
ejpam-3153	199	1	int	int	NOUN
ejpam-3153	199	2	.	.	PUNCT
ejpam-3153	200	1	journal	journal	PROPN
ejpam-3153	200	2	of	of	ADP
ejpam-3153	200	3	math	math	NOUN
ejpam-3153	200	4	.	.	PUNCT
ejpam-3153	201	1	analysis	analysis	NOUN
ejpam-3153	201	2	,	,	PUNCT
ejpam-3153	201	3	8(6):273–283	8(6):273–283	NUM
ejpam-3153	201	4	,	,	PUNCT
ejpam-3153	201	5	2014	2014	NUM
ejpam-3153	201	6	.	.	PUNCT
ejpam-3153	202	1	[	[	X
ejpam-3153	202	2	4	4	X
ejpam-3153	202	3	]	]	X
ejpam-3153	202	4	ds	ds	PROPN
ejpam-3153	202	5	kim	kim	PROPN
ejpam-3153	202	6	and	and	CCONJ
ejpam-3153	202	7	t	t	PROPN
ejpam-3153	202	8	kim	kim	PROPN
ejpam-3153	202	9	.	.	PUNCT
ejpam-3153	203	1	daehee	daehee	NOUN
ejpam-3153	203	2	numbers	number	NOUN
ejpam-3153	203	3	and	and	CCONJ
ejpam-3153	203	4	polynomials	polynomial	NOUN
ejpam-3153	203	5	.	.	PUNCT
ejpam-3153	204	1	applied	apply	VERB
ejpam-3153	204	2	mathmetical	mathmetical	ADJ
ejpam-3153	204	3	sciences	science	NOUN
ejpam-3153	204	4	,	,	PUNCT
ejpam-3153	204	5	7(120):5969–5976	7(120):5969–5976	PROPN
ejpam-3153	204	6	,	,	PUNCT
ejpam-3153	204	7	2013	2013	NUM
ejpam-3153	204	8	.	.	PUNCT
ejpam-3153	205	1	[	[	X
ejpam-3153	205	2	5	5	NUM
ejpam-3153	205	3	]	]	PUNCT
ejpam-3153	205	4	e	e	X
ejpam-3153	205	5	lukacs	lukacs	PROPN
ejpam-3153	205	6	.	.	PUNCT
ejpam-3153	206	1	chracteristic	chracteristic	ADJ
ejpam-3153	206	2	function	function	NOUN
ejpam-3153	206	3	.	.	PUNCT
ejpam-3153	207	1	charles	charles	PROPN
ejpam-3153	207	2	griffin	griffin	PROPN
ejpam-3153	207	3	and	and	CCONJ
ejpam-3153	207	4	company	company	NOUN
ejpam-3153	207	5	limited	limit	VERB
ejpam-3153	207	6	,	,	PUNCT
ejpam-3153	207	7	london	london	PROPN
ejpam-3153	207	8	,	,	PUNCT
ejpam-3153	207	9	1960	1960	NUM
ejpam-3153	207	10	.	.	PUNCT
ejpam-3153	208	1	[	[	X
ejpam-3153	208	2	6	6	NUM
ejpam-3153	208	3	]	]	X
ejpam-3153	208	4	p	p	X
ejpam-3153	208	5	sun	sun	NOUN
ejpam-3153	208	6	and	and	CCONJ
ejpam-3153	208	7	t	t	PROPN
ejpam-3153	208	8	wang	wang	PROPN
ejpam-3153	208	9	.	.	PUNCT
ejpam-3153	209	1	probabilistic	probabilistic	ADJ
ejpam-3153	209	2	representation	representation	NOUN
ejpam-3153	209	3	with	with	ADP
ejpam-3153	209	4	application	application	NOUN
ejpam-3153	209	5	of	of	ADP
ejpam-3153	209	6	stirling	stirling	NOUN
ejpam-3153	209	7	numbers	number	NOUN
ejpam-3153	209	8	.	.	PUNCT
ejpam-3153	210	1	acta	acta	PROPN
ejpam-3153	210	2	mathematica	mathematica	PROPN
ejpam-3153	210	3	sinica	sinica	PROPN
ejpam-3153	210	4	chinese	chinese	PROPN
ejpam-3153	210	5	series	series	PROPN
ejpam-3153	210	6	,	,	PUNCT
ejpam-3153	210	7	41(2):281–290	41(2):281–290	PROPN
ejpam-3153	210	8	,	,	PUNCT
ejpam-3153	210	9	1998	1998	NUM
ejpam-3153	210	10	.	.	PUNCT
ejpam-3153	211	1	[	[	X
ejpam-3153	211	2	7	7	X
ejpam-3153	211	3	]	]	X
ejpam-3153	211	4	hs	hs	X
ejpam-3153	211	5	wilf	wilf	PROPN
ejpam-3153	211	6	.	.	PUNCT
ejpam-3153	212	1	generating	generate	VERB
ejpam-3153	212	2	functionology	functionology	NOUN
ejpam-3153	212	3	.	.	PUNCT
ejpam-3153	213	1	academic	academic	ADJ
ejpam-3153	213	2	press	press	NOUN
ejpam-3153	213	3	,	,	PUNCT
ejpam-3153	213	4	new	new	PROPN
ejpam-3153	213	5	york	york	PROPN
ejpam-3153	213	6	,	,	PUNCT
ejpam-3153	213	7	1990	1990	NUM
ejpam-3153	213	8	.	.	PUNCT